{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299792458.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6.62607015e-34"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import constants as C\n",
    "print(C.c)\n",
    "C.h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9.1093837015e-31, 'kg', 2.8e-40)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.physical_constants[\"electron mass\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1609.3439999999998\n",
      "0.0254\n",
      "0.001\n",
      "0.45359236999999997\n"
     ]
    }
   ],
   "source": [
    "print(C.mile)\n",
    "print(C.inch)\n",
    "print(C.gram)\n",
    "print(C.pound)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.0\n",
      "1.7724538509055159\n",
      "(0.49801566811835474-0.15494982830181012j)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.special as S\n",
    "print(S.gamma(4))\n",
    "print(S.gamma(0.5))\n",
    "print(S.gamma(1+1j))\n",
    "S.gamma(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5905.220423209181"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.gammaln(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1+1e-20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy\n",
    "from numpy.lib import scimath\n",
    "scimath.log(1+1e-20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1e-20"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S.log1p(1e-20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k =  0.6134953491930442  ,b =  1.794092543259387\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import leastsq\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.array([8.19, 2.72, 6.39, 8.71, 4.7, 2.66, 3.78])\n",
    "Y = np.array([7.01, 2.78, 6.47, 6.71, 4.1, 4.23, 4.05])\n",
    "\n",
    "def residuals(p):\n",
    "    k, b = p\n",
    "    return Y - (k * X + b)\n",
    "\n",
    "r = leastsq(residuals, [1, 0])\n",
    "k, b = r[0]\n",
    "print(\"k = \", k, \" ,b = \", b)\n",
    "y1 = k * X + b\n",
    "plt.figure(figsize=(10, 5), facecolor=\"w\")\n",
    "plt.plot(X, Y, \"ro\", lw=2, markersize=6)\n",
    "plt.plot(X, y1,\"r-\", lw=2, markersize=6)\n",
    "plt.grid(b=True, ls=\":\")\n",
    "plt.xlabel(u\"X\", fontsize=16)\n",
    "plt.ylabel(u\"Y\", fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.03662651)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def S(k, b):\n",
    "    \"计算直线y = k*x + b 和原始数据X, Y的误差的平方和\"\n",
    "    error = np.zeros(k.shape)\n",
    "\n",
    "    for x, y in zip(X, Y):\n",
    "        error += (y - (k * x + b)) ** 2\n",
    "        return error\n",
    "error = S(k, b)\n",
    "error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "真实参数 [10, 0.34, 0.5235987755982988]\n",
      "拟合参数 [2.17992861 0.12322113 1.83112137]\n"
     ]
    }
   ],
   "source": [
    "def func(x, p):\n",
    "    \"\"\"\n",
    "    数据拟合所用的函数： A*sin(2*pi*k*x + theta)\n",
    "    \"\"\"\n",
    "    A, k, theta = p\n",
    "    return A*np.sin(2*np.pi*k*x+theta)\n",
    "\n",
    "def residuals(p, y, x):\n",
    "    \"\"\"\n",
    "    实验数据x, y和拟合函数之间的差，p为拟合需要找到的系数\n",
    "    \"\"\"\n",
    "    return y - func(x, p)\n",
    "\n",
    "x = np.linspace(0, 2*np.pi, 100)\n",
    "A, k, theta = 10, 0.34, np.pi/6\n",
    "y0 = func(x, [A, k, theta])\n",
    "# 加入噪声之后的实验数据\n",
    "y1 = y0 + 2 * np.random.randn(len(x))\n",
    "\n",
    "p0 = [7, 0.2, 0]\n",
    "\n",
    "# 调用leastsq进行数据拟合\n",
    "# residuals为计算误差的函数\n",
    "# p0为拟合参数的初始值\n",
    "# args为需要拟合的实验数据\n",
    "plsq = leastsq(residuals, p0, args=(y1, x))\n",
    "\n",
    "print(\"真实参数\", [A, k, theta])\n",
    "print(\"拟合参数\", plsq[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(x, y0, 'r-', lw=2, markersize=6)\n",
    "plt.plot(x, y1, 'g', 'r-', lw=2, markersize=6)\n",
    "plt.grid(b=True, ls=\":\")\n",
    "plt.xlabel(u'X', fontsize=16)\n",
    "plt.ylabel(u'Y', fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 56\n",
      "         Function evaluations: 73\n",
      "         Gradient evaluations: 73\n"
     ]
    },
    {
     "data": {
      "image/png": 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2LlmH/2Id5VeB+cbAPNH6sZX6hHn8lp/5Q7C7UxD0FUos6AvSEZqpzV462L/n/PXPp7B/x/1/8Gc2uP7RXZQ7hHf9+u8BUO7Yjjn1NdtRuZ1LH/wIsqko7mp2/8Z99v83t9C6wumrwK9o1s8I/AOwKvwzR/oH22Y/tXJKENgcK4CUjIWBYv3nthm2MUZJPQ1H6bpXCevub8r9yYV3VlnVjcX3YzP+Tt2Javy5UP5O2tDOakFfIfPHHm8Cvrq8/8b5W7N9xLCQsoF9lK63Z9xwUb8Lw90/v503fvYgb/ynhzDHzgMgF9/Dez7zz+qxfeUnP86TfbtRm7D4+hJ5vcTtdqQrZs9Sq5GRv9PgHyAK/6xiAFIO4KdhAFJ15oCB+toK28xlBk01BHMaAycpJb3q39wy9T7MAe/47aTPp2GeVfD9zm9jxLVveeWfs4+rkxD7r4/3YP9hP91NXnzGT3snsNimL0W1xWNnu8cF6L3C3uuX6rbvvPwy3/y//VN2XbkJwI1/6/32hDEUZ8sa83evqchfp/SbVUE/+8ff+MWJvxJIpX/wP6dkVQPQamtFH8Aq0cBTVwFzrARy2+qrtw5DsNVklWvNrTcHk2sszJOj+KeMI5Qtjfk7KUSD6c7oVHU8dXMdfp+b8G0O7B+xdQ2gBAqlKZXCGLs6OfHpB2j+P9746Pdw/QPvZt/5a7z821/gyfYN1K07rgM2jy6gUvyFmGZ/gSoaGGlm3GHiNz+Ncz1GaaeydhJL/ewnf0umNTbx9M/2/HAKaL9cp22YxQeQU6ev3lg/QO443I8+x3+yCs4fKoN3QuK3VY3amPq5kF36XLr+GBpnjmN3yn3Z8jN/X1Iz+7FBXxBP+GaPx7H/WOBX67yH/Rde4FehXN4fzeJBSfHIsP3eQ/ZcuAbA13/wuzCFYtujJywePbH5/g8UPHz/DkrdbPi+dMwf2rP9UGLwD7Tx/1Xhn7pOAv6JyRgKaPea1gsBuXpj6aBzrALGrgRWUX7P46pgLlhrTP05gvfGKv5kOxMMkMm8zudK+TtJBX2lsP8w6CvHAHSw/0jg10J0jf/72L+SNuXTZfyU3c1YT37+dQDMouDat70KxmAU3PvWXVz4z09QmqKK8m1TP/3IX42w1Lac9QkULfgHnDFwFE5FLvzTl/0z/jmN/8cooE27aQronD6AXEfwGD9AOP74+XmNgN/mXIYg9ve0ZF3jGNvOWL9M+nz6eejD92OO3SGMP9chnJItD/sUmOTNdtTN3B+Oy9nvluUlUtNDw1db3rRmsw7W0WJaYXSxDKFAC/tHK8odhvvfvmD3Hy1ZPH7CkT/+Otc/8G5uftNLPDrzgAcffAzbYbFRItpUgV92xy+X819RsXmq/QRitya27WMK/knt/NW01UAU7r65druf4zuA+eLomA09N49y6cYSbiUZO2evK5LfP0IFnQMGsnVWg4Jc+5AHB/ntOpkT1nmeVge+jB33mJVX//lpM/1cfD+H0fOOyu3jbkvh5eFJ8bhzE76168R3+/Lb82f/ofhJ3my/1azfywVk4R9H/TTc+Kvbuf++DfQCDpw9j9pcAnB/76uYcgNT2nQPftZPf/Yf0jx15JgTHxpKwT/+MVcuN+I3R+akgHbGNHIFkOx7pCN4nauAoT765HmDdOaQqSuFsZBb//lpanSq4l91xu9ky8/8ffFn5e0Zup39u925/KAv3yFcYHef8lcMqY3e7W5e1uFbO39FWrt9WeOhUUZYVDPzBZUDFs1SlA3+clCIVrATrvz4TuT2TtQN0MVluHEGKTcwl8/A6bPoQgAb9WuMMy42iAylUdWr+7w0BcqVEyz8I4YNVTaOYKyLGqCsjVV343fAXn+1EgDqvX/9GT/GK1uVcbN/+7kxnjEHcGwFkNoH2J81hzt+uR9GE1DWPh9zmKZWAH69VN26jZ5Zemq3sJx2Y304yV0RxJTKO8HZC6uvSOZS+LZMf1tj2Dww3bE7RfHDiJm/iPyyiFwVkS96x/47EfmyiPwbEfmUiBxI1H1TRP5IRP5QRD43aaStQceDvrLqJqigtt029m/PhYnfYknfuhu+hCmf/bTPShnMAXj8UgHHbmG2PQJAHuyF24dAC0ZT5/3x6Z6tV+IrASc+3x/is/+67AgHcEqy2BEzrQDGPvA5foDcuq12epf086wE/L6mrAj8vp631cEc487F8/3+hsv1/w5ysX1I+59i9fvqjXmmYRzs8w+BjwbHPgt8mzHmO4CvAH+7p/4PGGO+0xjz2og+a0Ufd/BOC/pqBXsloB9/o/dO4rcI798vFyZ/azF/pNn1SwqDLDQcvdxc1PUTmAc7MNVOX7qCfwxQ6i7UY0w+/NPH/klJGAls60wPAHNtdvtpGyK/r+Z42gDMtcNXnyN4ChRk667mRBzbX448Syfv0xrTFEf6cJl+gz72e0nBPKsEb+VK9kiNMb8N3AyO/boxZll9/JfAmRnHRiw56RxBX6k6fdi/ez+E/YcZP90x3/mrHP1TDKKAvXcxO+81l3zxJczS4v427XPz52/64iJ/W4FeQSBYGTUGbQVtj8XZP/X5iC9gFQPQtOsbhbRyDfuMlptgAFKzpdRMbJVVwJA8CyMQ63+dhmHdfYyZ5Ydj6i8zrPT7YJ5V4JqxM/5nQfX8D4HPJM4Z4NdF5F+LyCf7GhGRT4rI50Tkc3dultUgu7P/nGyf3fPBZu3BZi+23fZG722658CGLz704zl/XdoHN/tfOANQWP6/LAwcryJ/tz1BnuyAqycwS4UuJbnpSxj5u6wf/HYsQBk1Bu3UD058AxClfFYP3lgHcC4FNJYF1NaPG4ChH0J2ds8ZDcCQQzh3JZB/b1Xnb27pU9pj/uaWqdedO6Z1Kf2cGX+OYzdnwpOSWZ4SEfkvgSXwPyWKfJ8x5kPADwN/U0T+XKotY8wvGmNeM8a8tv9QN7oWaDF/pgR9pTZ76cP+e5O+DWD/bhXg4J96RaAM4v52P8TsvQ2b2zC73kZuH8a8vdeb/Uu96Ytj/zjsfyjxm5MU/BOmaK6PB0o/Bv+AfUiHZv+uzfBYfW7FFcDQQ7+KARgLA4VjjY4nwwjk9NPX/7oMwbOWVa5tDKY/Vem7fqLHM2GenLqrKH6YQfmLyE8Afxn494wxUfzFGHOxer0KfAr4cG77KdgmLDMm6CuUubD/zmbvHYPgHL+V81eZ+k8KA0ev2IbFYDYewaXTmCcLG+XrqJ/VLl/GtOGfMPJ3DPwDbYhmKPunOx5KjgEIJccBnLu5ypDzK9cAPI1VQFM/f+k/h8PzeTQGc4x/LqXvxjOlnzEwz6qTmxxZ6UkQkY8C/wXwcWPMg0SZ3SKy170HPgJ8MVa2U7d6tZk3045fJ+FOX05ivH/7mjIa/QbANyIh/LNQZcP2kbKe9S9Ed9I+FEpTFLqCfwyy8zEcvAH398GBG6ALuPgSelOaDV/KKrtnqTqRv24LyCnwD7Sdv33sH98AuB/kFPx/KAlczl7Aqy6LUz/WKauAVRzCY1cCcxqDrWAUUmN6WuymXKU/FuKBfJjHtROr31cvPD/7No4i8ivA7wHvF5HzIvKTwM8De4HPVjTOX6jKnhKRT1dVjwO/KyJfAP4V8P8YY/5Jbr/twTYGoC/oawj7t2106aIp7D+sE0sZ0R5ne9Yfo3w2tM9K8Stt4Z+jV0GVcG8/HLqK3N+LuXG4gn+a2b/D+h3c4/b8HYJ/hlI/QxD0FYF/AEIICMY7gFt1B1YAfn2/Tb+fWFux9rLTOqTGMWG5D/krgTFBQ3Pi6X0KeFXjsM62fRl7L1ZV+q7P5LkRMM+QY9fVTbU/9tqzg7yMMZ+IHP6lRNmLwMeq928AH8we0QhJBX21y7R3+gqDvpAmoCj8ghWGEpfWocr8SZPp0wVfFQhUwV4IrfQP1icgteLXAfMHrSiVxhiFVmA2Sjh8Dbl2ErP/BmbnXbh6ErPrPnrfQxQarQURi/2DolCapVb1XsJSK30F2OCz1nUiYGzW0dK4lA/dnb+QJujKT//ggrXczmJ+AFiuxFJApLKAuu+x20Y8ECzWViwdRP1MuGPEU0JAd5IRq++3A+lVqnvO+nf58p7RTBnqd1V51quDmEw1erkGdthYj1P8U9qpx7Iixh/K1vs2Awmx+Jikgr7cD2cs9u82ewn7jWH/7Q1fGuzfBXn5s/9CLOvHT/ugKujHwj8laqGRIzegeMzG2aO8+mt/yuLxksVXzqDvV07fxJ6/DvZxr6m8/+0Zf4Ppd+IFImygFAPI1lf17MOHg9qf28nloP1D9BlAOT6AVVYAsTJjYCBXv88fMNdKYOpqYF0sm2clU6/Lv4+5M/0hiKePyTMG5hlL5QzPT/2Ot7byj1xPH/afCvoakhzs36d+2jpB6uehlM9ezv925k+7Eqidv2IQXXL8i2dZbt/FwwMHOPmFr1Fu7GLPvziGXhLk/bFGwFf8Y+Cf+n2LseMrV48VFCpKz3BMnYWMCQLLZQGFVNBW2QxHsGun00+m4zqnrVa7mdDHWCMQjuF5NAarjnvMPcszxuNn+rkwT18buTJmdba1lX8lfbP/oaCvMQnf+rD/dvvjsX9X3lf8sbQPogz7/nTJ3vM32HHrLle/5V3svHWXg29e4t6xE2z7+h78yF8/8ZuBjqJPsX+AjjGANj7fPzOPM4DSeP90CujYFUCnbI5iHWEA1rEKgPFGYKoh8MezlQzCnGNah9KfqvhT7Q21MXbGPxaWey6Ufyhjgr5iktrsZahO63VF3r+L+m2nfbB/Oy+XLDbh2JfPojcWvP6RD3P0y2+x7e4DNu+9jH684UX+ulm+m51LJw9QCv4BOsYAug7fEP7xDcA4yucwBTQWBNY6n5j9++26vuZaATzNVQDkGwHb3uqGoGnr+Y7wnXIv5lD6qyr+HMfukPjX8Y7ezCWUsUFf/vHY7D3E/mObvbjXHOy/xv997F987F+zqKJ9i0KzeRT0AnbduluP6dIH38vpz38FTIF87Qzlson8tdTPgmVZtDd8ITQA7VXBpi6y2D9AywCkAsBadNBA4ddlEwYgpJmG4ivrkALatwIIDUAOe+JprQLmWgk07ebj2mOlT2mP+Zt3TOOvN5dlNFXpu2ciBfMM+aVcG3199c34x3zvW175K2nP8ucM+or1lcL+a8y/B/sfk/ZBPLhHvAhgpTQPvlNhFmCM4ZV//kcA3D15mGJzk6Nf+jrmyX64fqSe+bvEb272nwv/OAk3fh9K/1C/9zB/X2IGwP+xzbUCyPEB+P2F46vLZziCY+349afQQl2buUZg7LJ+XYbgWcrUa8qH1NYz058C88TKhO1MVfywxZW/1DPteOAWzBf0NbTnb7z9Nvbf6sODf/x++tI+qGolwC7DtY8XILDzdjP7v/It7+LQG5fYdeMW5spJ9P2d0cRvY+GfdrqH4IGcGAA2VVKGpukr9QPLXwHAagagzwhEx9ajMFLjS8lUXvw6VwXrlFXHPZfSh35DPhbbn+KH6lP8Lclk+j4/TwHd2f+qQV+pnD+h0vfhn3D27xsAH/v34Z+FKuu9flUV7etTQGPUz81XAa1hqXn/r/4u+85d5e7po9w9foj9l98ApeGtVyg3VQv+0RUEFIN/GvpnuCpo7xIWY/8M5f8JDYB7wH3Kp63Tnf2nKKCub2j/YMI8QDnpoP0+m7p5M6+xvoCpRmAMRLJqkFSoVJ+VcZh7HGPvS+5MfwqTJ5fNM8WxG874m99J/uTruVL+Q9JKxTwC+09JLl3UQUB19s9UimnPQNTMnwT1k91w74MFZgHKwKk/eJ3tb9/nygdfZXOf4sC1N+HxDrh00kv8VinuCfBPm+8fT/+A116KAZTj7Ez5A3zJWQHkRgIPxQJMXQXE2ssaX+7MbwROPne07JBSnutvDply7XPM9Mco/VR7Yx273f7aE6ExsuWVv4+n50oq6Ks+NhD01Ur0FkBPfdi/X78P+3fthGkfQurnjb+y4M53L9AbgBiO/OkbLHdsZ6lPcuL3b3Lg3GW4eZTy1l50WXH8e+CfNve/Df8AUfgnzP7pSwj/1MczHMB9+H9sBeC3HZO+FUCnbIZCHWsAxkJBrr25jQDMbwi2okz3g+Qp/bkgnr72pjh2czD+2XP7bD5XycYAACAASURBVBVJQT/RshlBX1M2eu+ej2P/Y6ifhbJqtkX93IBbf2mDr/7Mbl7/W7vZee8hB85d5fbLx3m4bzdHv3yObXcfIGdfRj/ZoKy2ffTz/rfw/Sjk0x/8BV2nUgr+GeMA7vvsy1AQWK9yHVgBjGUCpcr5bcakbxUw1GbY/ljGzDvJEKyq8OdQ+lMUf047Y4O7whn/2Fk/PCfKP5z9xwxAbyCYN3sPg77CPvz3Pvbvt5+L/Y9J++CO+9TPOuvnhmHHTdv/kdfPUzze5MoH3oUYw6kvfA2jC8xbL1EuVWUAFH7e/5bz11TYfwT+Weqihn9S7B9oGwDfH+CkhfkTxAYMKM6+FUBoAMb6AGL9D8FAyeX9SF9AX1tDbab6WMUQbFWjkBrjuhX+Kko/16nb9yz1tdk34y9bv7v+5yuUrfXNryhDQV9Nue5mL6GEDt/wWExC7D88l5v2wVE//ayfLKq2lyXHv3yWx/t2c+vl42y//5D9187BvX2Ya0fbmT9Hwj9AXXbIALiyKQewLzED4B7wPgpoqw3PAKziA4i1nwsDzeEL6GvLbzN3JjgHh34uhTtHn6vImHuRc4/nUvpjxjDE6MnD+POeheysns+TuAyfCpu1szSKAhP9shS6/oJtls9GwSnRYFSrnqrbtpk+Mcq+oiiNVeph/TBjqK3bZAVVokBpFtj8PIUYUJpSCS7r5+YZwSyAJ7Dnyi12X7vN9feeYff1m2yeuI3ZdRAunaTccw+1z+4HXCpBKqWPqrJ7aoUqjH0VU2X7rJSuCApTjVXX1xJm/6S6T261o40MZgCdKiXtfkKjmmo/zAbqt2PbamchLelmBbX1221rVGdikSrrnptkds/quUtNVFLtpsR/TufK7LnVVgahjDV6uYq5H07Mh3hSbeXEkeQq/qlO4639zeLn2xmGfpJtJLB/pxiGeP/+Xr9he37ah27On5y0D93c/9GsnxuGyz9aUG4HvQFHv3IWRLj0oXdx/10LOHIRo0rM2VdYPlnU8M8yyPypTZPxc+non97sv9kQvnHa+s7fnP1/3QqglfPHcwA7CqitE1I+YysCH7vvrgD6YJqx0cBT2UCpsql2w/ZyVgJTVwTriK59FjL1mnLvXU507pjZ/pwwT47iH/N8wHOg/H3JYf7kYP9+W+PH0Mb+oZ32wTcATvrSPviGIEX9tJG/hs2X4OxPF1z9yILb362RPVd5vOsgPNgLhYYTF+DxDvSF073wT2sDmAik4yCfxuHbwD/uvDsecwA7iWH+vuRRPtMGIOyrjwnU+tzjCE6NJxe/jZX1213FCPjtj3UQ+v0/L8ZglfGOMZaDxren77Gz/VVgHtvG8Iz/HcH2cZeZWsLmzP6jxyKzf9dOaqP3VqbPaNRwO5K3qR9QQDPSPnQSwNX4v0F2wL0PFNz+UEF5+gZm4zHcOAGlwM77mIPX4cYRytv729z/gP3jgr9iqZ+B2iCEe/8OMYBSDmBbN+0A7osBiBkAv+8cH0CfAQivJ+y/aSPeT0xygrlSMtYITDEE/ji2gkGYayxj7keO0p9C31wHzGPbmGfG72RLK/+p0gfPtMulqZuh0g4l5P27PnzIxy/bMg4ZaR9C6qe/4buITf3MwsCxS8hyG9w5Alrg4FXY/hDz1suUj7Z5WT+rTd/76J+mPYt3x6AxBsBaHMDQbwCc+AygOVcAfr/N+XwDMJYWmmo/p91oWysaAn9Mqb91tbty2yOvPee+zjXbj5WPXfMcM/6xgXPPnfJPYf994mb/fsK3cPbvl6nrtWCc5nUI+3fjTGL/PWkfUtRPf8P3YlFSFBpZaNh3F7PnNtw+Ao+3AWBOnMdoRXn2lZr+Wdabvlus39/43b0ujWJpisYX4ME/ZctAtA1CGAAWiwDuBH2NNABjfACtdiMrgCE/QF88gGt7LiOQowD7sOhomxN8BFntDijwdSn31hiCaxur8HNm+n24/qrfe6ztIcduzox/SrT0llf+uUo+lu8nWbZns5fePlr1+rF/9xpL+RxKGBtgoaFmk3e34XvhIoKrTV/cH0cv21w/N06CBjae2GN396GvHuvAP/7Mv7PzV2vWH3H4BvCPLds8gDEHsC0fU8yrrwDcWGMSOoLHSO4qYO6VQO5qYMz1rMsYPC2ZOvbcezV03/v6HRsD0qo7wrEb9lUG9Zo28w3tc/Uk5DJ/WnV6nMO5m73EmD+p+qEBCOv3p3xuG42a8w9B2ufmTwoD25dw+AryaDfc32fhn723YM/bmEsnKe/ubsE/IfsnBv8ALSMR4v/+Z1fWSQz+gWEHcJ8MrQCacvEVAIQ/nv4VgOsrNoZOnxNggFWNgGt/Cs1vKxuDqTN7X7J9JhlKv++7HYPtrwLzuP5ifUxV/DBS+YvIL4vIVRH5onfskIh8VkRer14PJur+RFXmdRH5iVGDHMkTD2f/dnbehXWc+EFfKlD6bedtPPDLj/b1+2ggn2bDmCHq50KVSernRtHe9EUVujIAGg7dxGx/ADdPwFKBEcyxCxhVUr75LsrNooZ/dED/dLCPMw4O/ukahrQB8OGfsQ7gVBbQLuUz3wfQZwDGOoKHYCDXx5hVQF+dsK8xq4E5jMHQ3xRZV9vhtefO8occuVOUfi62PxbfH6v417WT1z8EPhoc+xngN40x7wN+s/rcEhE5BPws8D3Ah4GfTRmJdUpbsccTvkXrJZy/LRgoVPyeAYi1M4X6GW76YuEfjRTG4v/HLkFZwK1jlu+lNJy09M/y/JlO7p+a9ZOAf8L0D0Ct8O37BgIa4wCesgIY6wMIj/cq2QED4PfflEkbgej4VzACff319TXVGAzJWGOxjtXFaOgr4/4NwTurQDwQn+3n4vvh+HKe+SEZ9a0YY34buBkc/hHgH1Xv/xHwVyJV/x3gs8aYm8aYW8Bn6RqRLJkC/XTaiNA3fQmDvlJjCNsYg/3XfWVSP3383236YlcAHva/6yHsvwl3D8KjHRb+2XEfDl2z9M9b+2vuv8v9U6dzMJLI99/2EUCleANcHrr8//p48DksHzMG/ZTPfB/AmBXAWBgoOZaBmWNKxhiBMU7UdRqCpyVTDVqu0p9qtHP7G5rtx/pN9TWH4od50jscN8ZcAjDGXBKRY5Eyp4Fz3ufz1bFBcWkZwhQJ9pympEmf4MoWosHYG+gfS33BqipfYlMrNKkBmuNKDBhd3+CiSu/gxuSnfShxKRzaaR8KU6UpEKnTPgAoIzbNghgwsFCapYaFapyyy2pslv5p00IUhSCCVegozEJjjl2Be/us8/fU1wHBHLoK9/egz77CcudDZNfjahzt9BKqMgD2Eqt0ENI8YFrseGzaBvuQb2CvEWeM6wfQpoDAeEa09dmmZdBIbQzd+9JU56p7VNKkXgiPte4/8VQQ/nH3DDjjrmmnayiNtFaAsbQQ9TNTl5HmmfAk7Ktuw/uRxkgG/nPaNwnxlUxuOoc+xTlEeFi3zGGcco3ikJEdMtK5/cYnDKvj+7Zt6Rwfk47jaU0FYncm+rSKyCdF5HMi8rnbN8vWuTH0Togzf4aw/7BceDyF/ftthm2HUb8+9bM1XtGdFYKb/S867B+7YmjYP9quADZKOHIZebIT3j7Y3OUT50Er9NlXKMsu+yfE/cvWjD/g/0cYQP5nJzkUUFcnBQf5s/1cFlBsP4BcR7A9Nx4GCsfYbm/aSmCobqzvVWiVMfx87tVCqo9V+hlz7UP3cwo8l6v4c2CelOJvtxuPcRmbh2mOb/aKiJwEqF6vRsqcB17yPp8BLsYaM8b8ojHmNWPMawcPebPsGSQWCfy0sf++tA9+P+Mif3XN/JFCw/47mJ33LPa/ubDwz8YTOH4J7u1FXzkWhX8MeOme0/APUCv8cAOYcAtIIJsC6iQ3DbRtq+sDaLXVw4CYAwbKhYLC/lrtZCi/Mdj53Pz6PoU99m8uGXuNqyh9Vz81jk5bGU7dIQln/EPMNr+/p5ne4VcBx975CeD/jJT5NeAjInKwcvR+pDr2TGVosxcf++/b5MW9z8H+XVt5aR/GRf4qMYgCCgPHLwICN4/bp0ELZt8t2HsHffFUTf/UAfvHQDf3T4cK2k350FLuvm9gIgU0JwZgqg8g1xEck3WvAnKNwLMyBM9KpgaNzaH0V8H2bdnuynJdM/4x92bUky8ivwL8HvB+ETkvIj8J/NfAD4nI68APVZ8RkddE5H8EMMbcBP4r4Perv79bHRstHQfvgOM3RvsMJbbZSyrffyrjZzi+1IYvIXW0mf3HqZ8u8tcFfsUif5WYhvpZlKiFtrj+wevIg/3wYLeF5EvBHLsIhaV/Lh390zS5f1pRv9WDv6wjgAuWumhWBx4VU+MygjafhyKAwxXAWAMQOxaygOaggsZgoDGrgKkRo+s0BOuKwF1VVh1fLstoHUp/DpgnNeNPTWDiij/vfo1y+BpjPpE49YORsp8D/iPv8y8DvzymP2gcvrF8/M25tOPXOmF154uOHWva1Z0ft+/8dWWsM9RzABo16Fy2ZV2efOtw1aaoj2OcAVFRKMgYRwG1s3+Aosr7r1TlFFVgjIFD1zB399vEb6feAGOgKDEnzyPn3k157gzyyjl0le/f+pEVIs65KtW9kta6xz7onpO2cpIX3nX5jlN7j7oOYOX1Y+uozj4AU5zA/jFoO23HOILttbvzjgTQdgbXz4J3b+rnwRN/bKG4a4vJkHPYb8PJlP0T+hTsXLBrTl+T2huxessxqNHjKzh0bbvjaKY5jJ6+yVCOPFebufQxf8bU95Wzex81LhXDp2M4pLthS7euVepFdd4xfzCVEoSaBaSMqQyJW1lULJyKbdNsCmPQ1cx/qRWCjfx17J9SVYpHVSyjDQ3HLiIX3s2B3zvAka9dAoSHx29z8buvYa4fpdx7l+LoTUBZ9o/SGCMYMc0mMCIoQ83+sRu+NAwgqxucgqfzuWbzGOndBMZJR+FnGAAnqxgA+530bz4TsoFibYR9+2ODuDJNMYNabQYGKT3G1QxBp70ttDJwMqfCH2pvbsXfR+MM2xhS/LHx5Jrq50L5p3bhWlXc7N83AEQMi79KaFYZXeqnpk0BVZgauqgpoGJa1E+3Yhmifmpj0FpYKI0pq1djZ/ymUvY2949l8gCYBWx79DYbV29y5+Rx9l+4xbZHj9l5xfDKb17gze/fg37rZTZ332ex84ldURi7c5c2AkVplxFQG5waigJ8OuiQASBQxBjdGNGAAgqMWgHYi21m3LkGAPd9BDN43wDEFO4cqwD3zISSo7hzVwNhe77MYRSehkwNEHuaCt+Wn1fp2766VE5/DLkxMCmZw+H7TGUq9t8n4Ubvrv7QD6YP+/fHEu74VfeZoH7WDuNI5O+iSvbmEr+5vP+q0IiC479VcvRr5xFtuPhtr7LcWCAIi4eaHZwFrWz6h4r+6XL/NJTPKs7Ao4FGA8ACBzDQ+pxiDLnXoSCw6Oee2U+MGmqP9/3g0/hrDCNO+QNiYxrjD0iNISZTmTRPIwp3iqwyprG+kui5nu8kNdNfx2w/5dgdeubHyNb4xkdILCVzKGMSvvXNnMKN3l29Id5/bsrnpk6j3GPUT1cmRv106R7am743ef+33YLFZsnhNy+yuWsHb33om9FKgYGdNx5jKvpnefl4xfypcv7oNtsnmv4hygBqK+owAjh0xsYooC7OwG8nxwkcU/Z13wkD0OcI9vtprmH4h55SCOs0Am5sq1AqYwZhHUYh1c+UvsZc81Affd/BGIhn1Rm/fzxO8ex/1nNxn+dG+eekaB7amrGP+dObziGT9x+PGdD0UT+Tm79kUj/bNFDH+df17L/cbsAY9l+8zv6L1yi3b3DtVRtc/fiw2Oyfe+/Y7J/3dqEruqdj/rRz/aTz/wCtY7EEcE6GKKBOxhoAX+ZaAfj91G1nOvRSfaShg3mMgBvjXNz6PmU95W9VmaLwh5R+32x/Fafu05rx9xqDhGx5zN93robMn6mO304fHvbvnLdh26Hztw/7x3Py1rivl/YhxP61sYwll/bBfo+6g/07A7EQ7aVaEHTF9tEV9q+1ddwWhXD7e4XDvwViDMe+eh5Vam69dJydb9/h/slHoMEcv4g8fC/LN96N+ZY/QSnLHLLBX9V1KY3S1imsxICmdgZjFEtdXUuGAxioMPrG+V1j/uFnEpj/gA/ApX5o8P54Ogj3Xfo+AFu+6wewz0HbF+CeH1sm7Qvw24L2jzTlE3DXEUqoQIbgyJSSfNbpHIZklRXMYJmRs3xbJ3F8BqWfPudPWGKTmC7uv66sns9EVGLm3V+nH/vvkxjvv243A/sPx5Eb9etm9rZMT9bPCPwTT/xmePAhuPPtVv8aDIe+fpGNhw+58q0vQ1lF/ypL/+TxdvS5l1rwjz/Lb+H+NBlBU/j/VloBQJoStwoMZMcx7AuIteWPZepqwI1pVYx8zujbKbJqNHDuPRi6n2MdujGIZyrME54bCt6Kxra8k2b+Q9Lh9tPl6MckJxagKbsa7z+s5yig2hR21knRWgko47GEotTP6rOouoxtu3pVTXlTwO2/WHDrzwrFdcXmTkVZXoQLryI3TmKOnsdt/s6Ra5jrx9jcf4eNw7fRytDw/hWqKFlqVbGPpJX0zTF6HP+/iWWwP5Lwcw4FFKhZQeGM38nUFYDtJ84ECiWHDqppJ4iz5eK0UDuubl8xemhTL80Qavfpr1bHzeyHFO4qK4V1GJcxim7IgD7t2b7tc9yM3z+eChwcI1ta+ce+rjmDvsbw/osKogi/dHc8xfuvYSCwyrFSVi44CholmEv99OGfZQWLJOGfwlJCy12KzVOgSwNPHsKhq3DzOHJvP2bfHbv5y+FryL29NvvnrgfIrscYZVrGRsTU9E+UtrP/inXkG4NlBYnVDuBWwBf4FNDmsxoMAnMGAO/7ShkASME9bQPQHB8PA7kx2CtwEF+XFmrL9VND2/cnTmqIPfMpiSmDVSiez3J1MFaxTVX2Tf35lH7YXp/S98eWXqm24Z82K+0dSPWMQT85zJ9RfTiHcISyWfcpJjoDGkr70PTRTvtgy/ZTP3vhH2nDP34OIB/+cewfVRib++fwNcz2B5ibJ5AnG1X+HzAnz4GWFv3TT/9gTJP/v6zy/yc3gPEgFJ/+GVJAneSmgYA8CGiID51SEGNgIL/Puk4CtkhBQVPgoKb+tARnW4neGZOp48yBdfruaR91cwrE49rs6y82tlzF3x6PPZcLkm/db79H5g43n9LPKth/vK809bMuE+D9rkyo9Iv6vc/+sbl/RKqNXwrg2AVA4MZJpBQL/yw24YRP/2yyf2pDkgEUpXsm8H97rj1bCTH4MBbAf59rAHwZCoEPlcIYNlCqz1wD4NpcxQjYNsbn6Xla9M519Z+bA2hOpQ/x2X4M5smdSOT5piIO34xnPyVbGvaBdnSvz/wZKj8V+onmAarbWB37b6V7cK+VsqtXN3UKCB/+Udake/CPH/lbt42N9E3BP1Bl7RSN2fkYDl+G66fs7l/7bwKC2Xvbwj8XT1HuuYfsu0+VgaLKJ2ThHwM1AwhV5ROqvie0u29W4S+oriHGAAIPAvJYP2EUcHVvYj6A2OfwO0zlA3LPjTvelB+GgervnC4jCPpZQbZs3Cfgt1u3FbmmmMSU4NgJ01ZdFYwxblOhHUgb6Skz/SkwT+p4H9Qz9jvbmt9wIDkc/9gPYZWMn0VQp2mjG/jljvfx/vtgIFu+/dqCkKRdN7Xnb+d9Dvxz8CZm513M7WPIk+1W92rBHL8IxbLe/N3f9MWlf44xgGIRwAB9DCAnc68AfBnm/aeVyhAXO8YIGrMSmLIasGPJWxHYtrZmFs8hGTtud0+mzPKhf6Y/t+Lv4+/nKH6XOTc8livPhfKPScwgjN3pKyUx7L/T/0TsPzftg3uNUT+7fTZQUGu3r2z456JdgVw/hWgBLYCG05b+WZ47U8E/DdZv3CvtDWCGIoCheYjHUEDda5jiNgcCGqKCpn5ofTDQkAHwx9KqN8KR6LedYwTGxLyESnUrGIRVxpTnH5lH6dvy/RCPHVM+m6ePyhmWT42lwfzz7ttzp/z7HL/rkinYf852j/77XgPgrT6yIn+94+LasIShZvavdLPz17YlHLkET3bCnSPN7H/HAzh8HXPjCOXNAzX/3xqARtEbaM3+hxzAuvqhtZ3AbZ+AO55KA+HOw+orAF/C40MGIBxXziqgzyG8ihFw4x1rCJr215/rP9XHlH5yr3VupZ9D4ex7Lvrw/aEZ/xR/V0q2PObvJIb952T7nAv797N15mD/Tlp5/h2uXJcfR/20l5qO/HWpoR3m7/L9O9O1KLDpGwpBRMAIWhSl1nDgDubBPrhzBNlxD3Y8wojd/F3u70a/9TLL3fcpdjyp9xRwGL/bXaymoCqNOMUugjYFC8r6M3iz/9rPYa+88Qm4+9jAaa2Z1AgfgC3X4PFDVFD/uBtrKyMpYbRu3B8Qxga4/ut6EX+ALdt+pvv8AmE/vqSU4lh23FZYFYxb1QyXzcX0m/LzYfvN+emO3dixdxzmH4M5esv3QD9TMn6Gs/qx2H/fGG3fPrMnTv304R93PDfyV6rZf73rl5f7Ryr8Xxz+f8Ti/HLlJKd+Y8nL/9eSQ58v4cg5Otk/AwaQo39GM4AmVgDQ/hGOXQH4521bwz+GXCpo7Hi4Csj58a/iD2jqrL4iaI9TscoKYd0Sji+P6aQG74O7j3PM9FdR/KnVZdIf1Qdlesdq6PWdCPvkOH5jx4YSvnXqhUZhTdh/CPm0x96Gf+x4GupnLvyzUNrOxGngH5cFtEn9XOH/20r23T6HYQf3d59g+x04+CXDy595ZA3Dvb3oyyca/L/a/1cbWvx/Y6TeAnKMA9hJ2ymsWvXseQ8+GgEBDVFBU47gPux1SAnEyqTGMJTWINcIrGoMnpZRmKPfnGvtu29jlL7rr1U/A/rLnVBEy/dBmBNn/E6eC9jH3xSlPhaBfuZO+OZLX9I3O0YLV5QBLLQq9dNeY4z6mY78VaaKuIUO/CNi0MZ+8Q7+MdrCP3Jfc/RLd1EvX+fOqaPsvvU2u96+x+Ih7L18k7sH9trsn3vvInvvN1tKVg+/209YG6m3giyr9BAuHcRSFyjRdURwPAlc+1iYBsJeTJsG6uiYKQjI3es+Kij0w0D2+4yda8M8IQzkl/HLpVIxdKjGweRiCBaK9en3mytbaVUwxphBvwO938AmYJ8JDv85YB473oGJjZv4uDFkgiVb59uNSC7SOMbhu8pG72FfsR9TuNm73+8c1M/syN8I/BNn/9hZv1KaHdcNpoDDb11k4+Ejrr73JcpFgSph93mb/ZPFEvPmK+jNosUAMpUT2DGA/KRvOZvATF0BuFcfFrIO5WrlkUmHy2f95ENBMVqoK9c5lphp2vGutiIIxzd2ZfAsZMpY+2Ad6L+PfTP9KRDPWJgnHEsz5uFn1x/DUByUL1v7CYiIr0Bzsn3mQD99GT9TyaxysP/UePrSPvjjiTF/mrLpyN8U/BOyfyz3vzEAeg+IAaUNx19/i+XGgquvnkEDy12AaJv988l2yvNn7IohkgG09GICQson0PqcMgCtpXSGDyD3oe/DT1vlehgoqWCc5nw/NODKrMsI5BgCfwzP2iisMoaca55T6a/q1B2kG2fO+H1INVT8Ty29g4i8X0T+0Pt7W0T+k6DMXxCRO16ZvzO2HxXMmgfLjwj66pZLrApmwP5j4xyifjol7tqzY2oUfN1/IuAr3PbRbfnonMHOADw5bljuBi2w4/5DDr91mfuHD3Dn5GHefl8BpcCOB5hD1+HmYcpbBxrs3zQBYI7+6Y7lOIDBx+2Hg8ByVgC2rbwVQMwR7EvfCsCd9yUOA+StAvxxxyQn5fFYQxCOKefvabWTuq4chT+H0odhZ37suemDeYYcu2ODt8ZOgmAGzN8Y86fAdwKISAFcAD4VKfo7xpi/PLb9Qkz9Jcew/7oc3WyfIb1zFakpoZnYPzAp7UOM+ulv+A5U9ElVzf51jbm7NBB+XMDCDqpOxbzUVT2lWRRSp2kQAbMBVz6uOPoZxbZbsPfaNR4c3MONd52C7U+Q8rFt+cA1zIPdcO4lyl0PMDseI6LqDKA+BRTXr6nGpSt/jdu4pjKMLguo9QnY6+r4BKC1GXzKB6Ck2pTdNCunZPoHL+jOlQH7PQ2nf0ifgzjO7/84+1JFOEn5BWDYN9C0kfjNZKyc+2Tdq4Qxhisn42ifY3Sqse5T+OH5ZPqGyGzfPz6E8ceCIHNk7m/vB4GvGWPOztxuUlYN+loX9u+fG4P9D1E/3auDeQpvVTAF/imUacE/er/h4o/Cub8GFz6mePAdFzBFCTdOQyk2ARzAifMW9jn7CrpUNf7vNnzPjwDuQje5K4A+HwB0fxy5zIlYRHB/8Ff3XO5KIBcOCscWk7EboYSz6CmrhLlk6ljyVkHp+zZ1pm/LTFP8OTDPGMUfwj/Piur5Y8CvJM59r4h8QUQ+IyIfGNNoHFOfpvRD6GdViWH/qRnYFOrnEP7v6rY/58M/qlL8LvdPUVhHcLkfnhwBdpQ2/cNyG9w6AQZrAIpNOHYJ7u9BXzneon+WphsBPMYBDO0fSOgTGOMDyKGCjoGBcp3B8fN5iqavbDjmlIw1BE3bXSW8qoGYs03/uoZYO1OV/hxMnr5nxh9jfTyDypl6psPx58psVE8R2QZ8HPjbkdOfB14xxtwTkY8B/wfwvkQ7nwQ+CXDqdPem99E+YxKDflaN+k1t+AINTOVTP/0xjqV+OvgnpH668YeRv0oMm9Wd6oN/6ofc7cqFpjCW+qm1gBjMAowWzJ57mAPXkdtHYcd92PW2xf93vY3Zcwe5fIJy713Yc59SqDOAtuCfCgJy9wJNaxMYRwF1BmCBo0NW97cFAdnrdRCQ++zDPSEElKKCumeq7xjkwz3+8zAEB8WihOv7U0kuJATpVWpKSaYmKUPytFYIYwzXkDHsg0Ny1jJUZgAAIABJREFUfTExX1B/DMj6YZ7wuDb5YbFzzvx/GPi8MeZKeMIY87Yx5l71/tPAhogciTVijPlFY8xrxpjXDh3qH15u0NccCd96GUG9juDuPsCuzljqp+/8DSN/x8I/dTs+/dMP/lI28tcmfzNw5Cpm+wO4eQKWGzYBnAGOXsQslpizr1BuLtoOYNNEALvPyRxAI1YATmIrAKBeAfizuNgKoC8iOMUGGhcANuwUzp19+uWHVgQ5KwPozqLHrhLmlKljGbrWvvs1BnaLfbe53/0UmCdXQsU/Rub8tj9BAvIRkRMiNqmLiHy46vfGmMZ96KfPtoUKdazkpHzwy8Ww/6lpH3yJUT9b5yP3Ywr8YxV/F/5Rzhj4BuDYBYxg8X+NNQBi4Ph5eLINc+FUC/83RuoI4MEU0N5noPM5lgjOScwHEPLt/WPR5XImDGTr9//QU+fc+VWNQF+dVpkRhqDuM6KEVzUQc7aZa+DGKn1Xp1t2mLOf7RsaAfOEVM5wQhOjeKbaTckssI+I7AJ+CPgp79jfADDG/ALwo8B/LCJL4CHwY8ZhAiPEZ/6E4kM/feyeoc1ebD/De/12+28nfSvEgIltDGOPN0t/09rj1733o1L9yF+30UsDISmgC/+492PhHwe9iFjlTSmYhYASu/nL0Qtw5WW4cwwOXEVKwWx7iDl0Hbl5lHLvXcyh263Eb5aNVNqOPfintQmMcqyfoopQLtFG6jG6B3Wzeg5iLCBVR9+2IaCWeOyg6hup77NjArn7H4OB6rIdKKd59lLn6u+btlLoYwfZsnFIKKwT1muVSzy3U/b0fRorhLEpC4YMYZ8RjZcfu4rrcfZmwjytYxlQT3OsacetrnNkFuVvjHkAHA6O/YL3/ueBn5/S9hBNM3enrxgts88A9EkO9u+X9bF/v28f++9cl4f523aMVZ9iauonUBkYh5cXFGLqdA+OjuqMgaNQKqxSNaV/HHS1IbujaKpq1y6jDRowhYH9b2Me3kTePgzb78PO+wiCOXAVc383cv4MeucD9K7HdfoHFGjtlLLY6zBiVXc1NvG/N6Hl4/BfocKcEz4A3wDYttp4/xQ/gG29axjAfn8+XBdmAwWS552EbdhyXb8A9BsCv16sbkxiSnaVTd6nyJTcNDmUxj7n51SlP1Smcy4B84TH/OO5GL/rr2l3HGT07EC+ERLN0JkJ70xlBaXq9AV+rQP774v8bdpo6KGuTYfnu/M58I+DgMRBQVXaB/GigFHA0cuYjUdw8xSUhdWzRuD4BTvrOPeyZft4EcC6goD8TeCTFFDTDQJLUz7jPoCQZWOPpR1ltn4+HhvCQKtAA7Ey/tjHwhdh3fFRsyrr72m1E7uePpkClw0FacXKDOL+3nOTTy/Om/GHv4XSSPIZSslzofynSF9K5zGSy4jwt3ucgv33UT9b5SKRv36bvlEM00D4zl/32dE+w9w/tUGIbf6yoStFr+DGqQb/Lzbh6GV4sAdz+Xil8NMOYEcBLbUadgAHBiCWCrr+3HIW5zMlYNj5FkZfDhmBVt2IcpnTCAzR/FaJrI22N5NSn2O8Q/dgrNJfFeZJTRh6n62RM37XTvhbyJXnIqunL0MRvzHsv98H0E/7tP3kY/9huz7232qzOg5Mon4CNfzj8H+3UUqB4PB+jFsJWDqlg3kWlBaOMYIpKxjIPWzKwjPGCGhFUWik2lBdi7Kbv+9+CEcuw7VTyK1D7Lt5DdFw7/RtNnfvgSsn0Lvvwb77GGPrK2VYQrW6UBjxsH6tqnFpdOsz4BtgD+7RBjaU3SQmGgkMnU3hhyAg992EMJC/GYwdUdwXAO3vMkULrb9r6JRJlbNl+zH+2I8/RTQYUqhjs4COlVUMUI6hS9eNGddheCdWLoXtw/wwj4/x+1CP9trRSDau8dwo/7ZDtuv4HZvCIVa+zwDEZCz27xxlsZ3AOtdYOYLDB1BVx21/znAF2Dim5fAtqGIPKl9AvUqoCPk2LXOTjqEQ618olPUR2IdOo1UVv4BCa4M5eJPi+i7K+8fY9fW77Lz3gIN/Arfed55bh96HOfcy+pu+Ahugte1TxBoUEYORJvUzWlmnswjKNOo+TANhG6G+jr44ALfqcZi69S+EDl/XZvPdhH4A21o3PbR/HIgagSEFH/oDwjKuHMRXrinfQLt+v58gJetO3zBGcme0cyj9WNnBlcCAgvePt1eLqyv++ly9Csi7V1vn251R+h7w1l66DsfPmOGk0j70Yf9jUz73929adft2/XLl23Xj8E+Y+rmmfVbHHP+/gX+cE9dQlJrTf3CexZNNrr36MlopVAkHXy/Ztv08bG6DC6ct9l8qyrKN//sQkDZNErilUaMgICcpH0AqIVxMcmGg8Ec9hRbqzufADqmy/rjHwiNjIIKnLWPG2XftDQV42j0e9N+E0F+CzbMuxe/3O9bhu+Vn/v6cLzpb96CfaMRtBPrJ2exlDMQTq+dTPxGLUcdm/7nUTwDL5mnDPz4LZgr8A5qFqn5g2t5RtwKgKCm16uz965LB7bokFFpz/KtvceFb38PVV1/i2BtvIQKn/sV9Ln/gGo9vH8Psvoc+cgsxhjJCATWmgKK05spbAVCNSVV+CX8vYKCe7WtTgIN/IiuA5vjwCqAPBrLtOKMfXwXEzoUQTj71s/ssh2X98k7iq8r45CLHAIxZLQzJqgYnj+WTLjMHvAN5M/3UuSlK328rNeN35Z5FhO9TlaGgr7EJ33Jy/uQmfYu2740ntW1jzuzff184Vo83+2+94m31mMH+8d+7TdntioDW5i81C6hqb8f9Bxx+6yIPDu7n6ntesSsALRz/46ssNh9gLp1GP9zm5f/xnLveNpDhCiBkAUHjxPVXAM1x1cz2I4yIMBhMm26gjH98KCgs6fjtUwYrOX37Z6v9Sm+6szecha/yN1Zyx913D9x9m7LqmjLTD8/1sXmGJHTspmb8/jOdG0H1XCj/VQc5lgqa2u0rJSH009efX3ZV6mf7OtIGoF3XMwA98I+f/sFCQbSyfyplePwujXvS9l27yeG3LvDgwD6uVAag0HDsq+cRA+bcy5iyUvYRCMixfgy0lf4IFpCT1I5guVRQX/pgIBjGd6N1EkonlLFGwK8ztLINlepWwffHMXz6r3UMfJbF8MmF+kbAPP5fN5K3Cze2nv1gxp+ilKZka3zjI6SlGAdm97nYf1O3n6cP82H/fp9TqJ8+9z9U+J1Na7zZv/LajeX+WajGEDj8v+H965YBYKfh+p836MLy//fduMWRs+d5tGc3V9/9EgZYLJ+wsXEJebgbc/WYxf9NlwLqsoCmDIA2XlzAgA+g9WNIrACg/UNKhdBD3Dhk/dgjCmJMfECq3FD5sF4u9ztmENZhFFL95EI6OQp/VaU/Zrafw+ZZBerpm/GH7dvXPAOwpTH/1CVMwf5jdefc7CXVzxD2X49/JPWzxTLx6/tYdiT1g2P/tH0BbfZPoTRixOLuVXoFU1No7TmH/z96v3DhpOLQP4Ud1wx7b97GiHDj5dPcPH2Cg5cuo3e/jdm4A9eOo3ffQ/Y8sBB8RQF1O4o5X4A2AkXZPNBijYuN3rUP+kLpJAsIYLPKElp/rb1UUHtvYpG/tcIPfAS+HyDE/PtooRBnBdXfNeOx/tizm2IMhZIT+/IsVgX5Bqv/d9tnJIbK9eXiyaJ1+pOFyARirGM3hvH70OdSv0Mx/zmhnzHbQOZARn0ZPzt1ajjGy9+fqDc28tdva1X4x/9bVPh/KgDM7NPc/Lc1pppK7Ltxi31Xb/D2sSPceukA5W6BQ5dgsQkXXsY8KZrc/6UatQLw2UGpFYATB/c0n5uVQYwZ0TfTTy3ZIT37ix0fCwfZPqewf9Iz4Fgb4d/Tkin9D13bEMOnD9OH/tm8O++fG6v4+2CeUPH77bm+Og7fiX6V50b5p2SM4zdLkcfomSOVfIj9D6V9iI01hHz896nI3znhH4v3N7CPv/lLodqZQJUylPsNVz6ieXzAYAQOXLrExpN7vH3oNDzahWCQwxdhcwMun8KUNv2DCZzApjIAzvHrp4FYjo4EllrRN5TPrm8g5Qj2f5gQd9b1QUH+8WdlBPx6OcYgbHPdfzmSM/4ch2+sfKtc8D1A+ntMYf4hxJOCeWLj9/vz0zV0nllvxt9AmM2qIXcnry0N+wAUAmWlE/1F/pigr9yEb6mMn61zMm3DFwvf2AfC3/Alh/rZ1O+P/HXXOhf846igKFp7/4pxmQM1hmr/XwPLk8KlHwGeCHpTQXkOOf8q3DwNR9+EjYew/zpy5yjm5l04eMdCVhUFVGtgQc0iskFmFeNIN8FsGgFNvRmMxmb91IZWNlB7/cGTI/4x2sehRQeN0T5rEU9JRKAgW6YxrhCBezLhICdjYSG/ji99kOizkrGwa87qIKdejMY9NNOPnYvN9MPjufi+OxaDeVy99gSngn1MYd+/k9g+xbxwvG2T+Cx73RLL+zOG+pmz56/fTwr+ae8B7G30EoN/aPb+bfL/6M7+v3Xyt20GNoBtJeb4OcvXv3kGSoXsvY7Z9gCunMY83NbM/IN9APwVgJ8Irm87SOgurZv3wczbWxlAuMRu/zhjP+bUsj62Ehic6Q+c98c11vE7ZpYdzrCnrBjW1XbOimGI0tnnxIW87yl2bkjx58A8Q4rfb9N/ftvXV/1eknexLc+F8k/JlGyfU7H/nHH0MX+S7Xtlc6if0f4DFlAO/OPOh8YgBv90Nn/xGEB1Qjif/6+qBHCFgR2PMcfOw+Z2uHUKtFj4xwCXzmCWNreQNu0soKWDfbS0EsGFPoAu3BNANfjlupRPaJR9DgwEcQOTCwU9DSOQYwimYPtDCnxOw5E7ztHsngyl78rFznchujjEk4IKY7N9224X5mnj+z7TLcD6kY5ByJEtD/uEEvA7apmS8C0mIfRj66b3+gUG4R8H18Q2fOnCVbq1WUsY+evG4Uf+zgP/UO8D4IzGgtLCUqq9+Yu4GYYYFoWdobv9f40RRDQYsfsAaIF99zBPriC3TsDdI7DvOnLwCtw8ZemfR6+hBUwF82hlr0Eq6MmIaSWCqx9+jwVUJ4LzIoEddKPE9OwB7D9Z7p4QhYHs8S7rJzzXhYlGwj2J8/UzMgALQR4DKNZGTOZeGU91KE9m9mRAO2G5QXbPgNHvXzUOwzy2T+kcbzt3VetYWbN93iGYv5MU9j9YL5PG2bfZS6y9OdI+1MaFOPXTGQCkeWCGUlP4id/C9posoLacG4+qZg/2R97s/GWVp938RUmVlkHa41OVAjZG09oARtlrksI6gDlwE7O5Hbl7BBaPYefbsGs33DwGu+5j9t63qRqU2M2+quRvpbLGxk8E1ySwq35QQp0MzhkBdz+VlJ5yJlD2bSqobbe7sUrsWEgJbe6X8Qy2bh8fi/kH5+u+g3L+OJvvexjrz8X4pyrrVSUXDkrWn6D0wzIppW/Hlw8H+mMN2TwhJBkaBB/STCn+cFWQI8+N8k/JkOPXl5jjty8fULvucD6gKeI7fxEoA8Pg999y+HorAegq/UKcI7e7kqgNkOu7mvH7xgBp3y8ldocwZahjAfB2/XIwkC3fZAA1RTW6hbG5/p9sh9snoXgC+68gj3diLp+B7V/FbGiMMnbmXxqUaoyArnL+lDq+Algo3c0GCt0fg+AZN2sACqlWip4BiK0Aqpbr+1F/R8EqwBkD3wi0jk80An6ZWDlfhgyBHV/e6uBpyBhoaKzCh/FKPzwfPkd9dODY+T7FH874w+OunT7Fb1rvo7egI88V5j/G8TsG+6/rTFze1rj9APaf88NKUT/r8xmRvynKq8sD5Dt1ffw/J/ePeJ9d/h/n/O1uAGOaDWAKAwttHcCqtA5gLXDoIrLcgCunoBRMqTAajNsBrPorjVRpILyHnK4PIL4jWBuLjVFBIVxWtx3BflSwa8tJny8gPB/6A8Zi/il82v8LZQzOvw78PqfdPsly9qauved+pcqkcH17HfGcTyns343f9WPbjyt+P5I3huX3Kn6a97my5Wf+KYjHP56CdlbZ7GUM9m/7yqd+Nth9P/YfUj/91Udf5K+7dn/T9+YauvBPzfevZvzOF+CUPFQPsvIUmIYl3ibw1QYwQCsDqDFgUBYWUoIxS8yJt5CL77YG4MhbsPcGcvcI5vY9zMHbGF0AJWIKlmBTSWB9AguaSODUCsDPBrqs7uHSRfw68eCeDhW0dZzIueFVgC8hFOSvpmAc5h9bDfhlw/J+HSe9sGFWxO80A9AnY1bVfXBrbIYfq5OL6dfnIwrf/xw3CP0wjw/ppKic0ETuxjD+zmcj7yzMfxTGPwD9DPa1Zuw/7Gdox6/YGPo2fZkD/nEGoPEFtPn/UClaqs1XqIwJoARQFXSEoiiMdRsXYr/DwsDOR5gjF5BrL8HtE3DgEjzchVw/idnxEHY8wSj7rRux5lMqZ3Up/T4Ah/krpP3MCN10EPVxe+eqK4vCQEo0pZH6XLNRPIRGIMT6fWW/ihHwy/jl/LJh+bBOWC+UVQ3DlHaHZOj3lavwY2VzlX54Lseh6/eXStPgn4s5dpu2G0VfGwOC2X+1Gs5F7mZT/iLyJnAXKIGlMea14LwA/z3wMeAB8NeNMZ8f20+O43dK0Nezxv7r9r2VggsKS/XfWQkQKBBvJdDUr25eD/tHOyVXGQNnANxqo/YH0Lw6yMjfDQylK/xRYbRBFdgdwAD23sVsXkVuH2Pv+YfsvXaeS+97D4uvnWL5rjcxe63x0GJVrVRGTASU0kkfgA36orMjGBA1ACqB9/sGwH0zVnTLAAC1cYg5fEOHsOszNBL+d7Mq5t9nCPx6TnJTkz8Nx2/uRCql8FNtZGH+EaguPDfs8I0r/k65wLHr1wn7Cmf8xjvvz/jLZwz7/IAx5nri3A8D76v+vgf4B9XraPENQH0sA/oZUvAhI6ddLr71oh3P9KjfkPnTaZs2XTM38jcF/wBoioAK2jYAqlZGtp7dV9cpMV3RHys6qDSbx7iNWJyItsddBLAN4KKCf0DtusaOs9u5e+g4O95+zKELl7jx8hn2fPEod7/rGmZh6xtVJX6rtoI0Big0urTwkBHXjwHdjM35K4wJjIO3KYxbKSDVTB1DGgYieq5vFeC+t7p2hBrqvmdfsYTRwn2GoE+Zx5Te0MqgT8bsYTG1D1/6lHxfu9nwz8iZfqpMCPHYvqbBPLn4vq/03WczAvZ5mg7fHwH+sbHyL4EDInKyr4J/CamB+sfXwVTIyfffHs8456+f9tlP+pYeT37k71DwV/SapMH5u7mA0gFgoQPYbQEpEGwCY1CFgcKw95zh0PkLbHv4iOsvn2Hj0SN23bnNvYNHOfo7O9n7VWmCwMJU0C7S13MCGxNxAns/lpgj2D8G/lLang8dvtD8mP2AsZhDuM8J2FcmPGf76jp0a4fgWAewVy9Wv0/CtnP/ciV3XFMcvKETt8+Rm+u8bxEKPMXeCc6KKP7weKfdhOKvU5sH52xA5LNh+xjg10XkX4vIJyPnTwPnvM/nq2NrkVUTvuXm+5+yq1ef5Gb99CN/52D/2D6b9pzCj+/9G2EASTsDaGMA3B4AjgFkj0th2HYXFqXh6Nm3EK258p53s+P+fYrNTW4dO8O+1xX7vyQVC6gyAqWidMZAN0tdFwnsJ4Nr7Q9sIvsCE/wIAwMAdAxA7EffOk+gEHoUh5OUEoqVtf2lWUApeGNICccMwhijMFbG9tdnTIaMYKtsj9J352Pv44n+0hBPDN9P5eWPTkx6Zvwu661rr94IyTSBXjkyJ+zzfcaYiyJyDPisiHzZGPPb3vnYN9vRSpXh+CTA6dMB3k0c4x/lEB7A/ofq1H2uGfuv+66hosZhmxpbO+ZhOvungaQKjw2kPGdwwzZyhsMFgDnGjakgIPtAUgd/+Q7gx8c1Oy8oFptLTnz961x/6SVunjrN9gcPeLxrF7ePnuDQGxd5+71YB7AxmMqnUJaWBSSChZqq/sRYx6/bf8A6rSsREG9G566/xev3yvbz/uPOYKD2B/i+gPpeJ7D+Du7v+Q3Csk6GMP858P51GoA+mdPJC/3wTnh+COKx77uzff+4Xz7E97urTH+V0T/jb8p5q11v8qNNfm6f2ZS/MeZi9XpVRD4FfBjwlf954CXv8xngYqSdXwR+EeCD37FhLKrblRjuD3lBX1M2eo9RP7tjGsb+gRZlsC/tQyryN7Xpi5/6YSz7Bwg2freK3F27cwY7A2Bn+iXopp4YAdVkABXAKI2IgzaqYYuwBB6+V7Hviwp5ZFgsNzl+9k1uHT/OvYOHAHiw/wA7HtyjuP82ywJMATZq2I7FGPdK7QMwRreygTofgHEObGXvicP6HRUUo3BZQWvp+AGgZQQizmC/rvuOG3F141h/OBlp+Q2Csq0yCYWeUpB9tNCYzLWqze0vlLHOXegqe8hX+H7ZmML3x5Sa6bsyfcFcsdk+NNRON4tfVnXdytXH+Et/R7wqNoaMCS3MBPuIyG4R2eveAx8BvhgU+1Xgx8XKnwHuGGMurdJvKuhrKOHbYLuZZadg/6m+wi0fh7J++mNIwVZ98E/LKRr4AlQwpk72T/w66Qygzg/goCG3FaSDgNiuufKXSu6926aAEGM4dPky+69eqcd569hJSjZACyxVBf8oD/tv+wBiEJD7sbgfzzKEgFowUPsPunAP0ML6h6AgJzn+gJRPICwblkn5B3Iw/yGZivNPwf5zoKD+gLb4PUtBaUPYf1Onmen7EE7rnP+8ZMz2+2Ae90z6in/pnud6z+sm4602Uu+LnYv5zzXzPw58qprhLYD/2RjzT0TkbwAYY34B+DSW5vlVLNXzP8ht3J/9rwL9rJLwrT2e+Xn/6TF3qZ8pqqo/46+PJ+AfByXF4B/o0j9t3938P1Zs/h+gTgHhKJ/aSJ32odR4DuBK+e0y3P4+zb1LcOx3FaoU9t24gS4K7h4+gikKuH0a2X7Wpogoq2WtSEVDVdV2kIIIXhxAicItmT3M0aWLiFFBqytx71oijtUj9vorqCc818BEXhsOKvNYQTE4yH6PXf5/ChJy5euxR6AhyAj6ylghzC1j4aQxM3zon+XHPg/BO9Cd7fvnw1l9itefgnn8ciGV0+fwt455pIc6HbrOv6+zKH9jzBvAByPHf8F7b4C/OUd/YwxADvTTx/uPQT/2fTfqtjue1aifq0T+AtPhH4oWp98ZgGaFYemgDjYBWhvAaNefavDqbgRwAwdpLWyegOt/Fg78gWLjHuy9dZVHBws21UHY3MW2s0fYffcGm/s0918S9B6XBVR3IoEd89QpQXExB+4mekrSUUF1tVIJYSC32rFX7QXCtZSLrr5fF2zmeppuBOw4+6cznfLEoSH/XkBakeYahXVINr8/U9mnyubg+fZzG9O3Y+zH9V2ZKUo/xPdrGMdT/OGMf+mcvNWMvyyVVf6ZsM/WjvCV4YtYBfvPlZQBSI8pPfufwv0Py7avszEAPt/fHzukg7/afH+82WuzUgizf7oAMFe27ifhAFZU3wFUeHwVS6C8VA3K8OS05vIxMEuBpUB5CblYwOY+nhRH2Xf/AdtvP2DPObj2YWG5H4yy4LsRhTbWASxibGoJbKyBfYyaYDCBjiM4GhBGNaHwlLM20sL7+yOApXO+3XbaCMCw0zc20x9aFTTPxbAzOJRVsf9JeH/P73aKwg/rjVH6rfMRpR+eD2f09fGwjUDxh47dhtFmJyT1/tYO9ikFo1W9NepTj/Bdt6Qcv2NlStAX9LN7wpw/kHb+jpWhLR/ngH/a1+Ibg3j6B+3BP74D2Id/HPNGi1WytVGonK4uBXSTw99+bpy5tuGD1y5yb8cGmzt2cv30K5z4+lcQXXLgS4rr312liy6MjQRWQCkoZZ3KStkfiotN0FintM31Uxkq1czKc2CglgGAjBQQbQMAtMq472IOI+Af8+v5devrGlgdxGROODMmfYq+HkPCTTlW6YfnY/AO9FM3c87nwDy+YxdoOXZbn7UHAXlwj3HBXaU1AO845Q9p7D9nn19f1oH9xwzAkAzN/qN9Bnj93PAP0EBAifQPDeWz+Vw7jrVVmA4O8iOAVbV8dXsAi9hvs4F/jL37VYoGo4Qdt4TtvMXld78fgMvv/iZOvfFltt0xyKZgUE3krzJUmd+q9qAotKWHlhbrt/1a57MBa4CkgX3GwEB28HhQTxzmcT9GbQqvbpcZ1I4UbpfJZf6klHpvBLnrbYXV8dySGi+kxxk7vorC98vMrfRTMA9Yto+DeXylX38uK7hnWcFCSwVaME/s61Nl+6xTigzoJ6+duDls7+XbLTO8FeTwUjiX+dPtp838GYr8hdXYP+G+v/77VACYH+3ryqcigOstH2sWEDUbqBsEpu1GMIX1Jxw/+3o9pouvfjOVd9fqx7KJBLbRwO100NpjSWhDzY12P0CHnfosizQbqBtdCW1c148O7kYAN0qjL1I4LBP218diiTk3Y8fDdmJtrlty+x9zbcMMn3ZUrq/Qy6BM+B27cq5M3XaCLeYr/vC4r/hbz6I3XjfDr/F/F9zotj51AZBL+3uQTekuXxPyXM38QxnL/Hla2H8f82dV569C92764vczBf4p0Pi5f+LZP5sAsHADmPpexRzAVLAP1hdgWUCqmYWjUMpgRGNMAWjunzHseQuKsuTQ5fPcPHEGgOtnTiH6ovUNFNj8PkYw4vwNFSxWTx5UnRDOjkHVjmA3Y249NwkYyOL9iScsmOkPrQRicJBfrr3pTOO/GYKF/DJ+ufB47Pz/396bB1uS5fV9n9/Ju7y99qruqu6uXqa76WZ6ZnpmPAMMCBgBgTACG4E1YMmEpNBYDmMLLMI2IkJ2SKEIKYgQVhhkPBYKhxTIyBYgwEIsMmgYEDNiZpit1+m9q6uru5ZX9fa7ZB7/cc7JPHnuyeXed2vt94t48W6ePJl5Mm/e7+93vr/lOLmRCiAmdbOQNhZ+rF+VpQ+dcfaLAAAgAElEQVTtnLlhvzbWvttfUtwBzRNz7IY0j2/x51SPDXtmrAzwDxVqDA3sXS63BfgnIqR2Kr+fpC9frif3Xx5XGeTnJbHM3zYrgOXtFfRPwVG7e5+kf1KvT9wfUFQAbeMATjPyKqBJggFoZeiizcfHdLc69K5Ab7DJ8tWLbB8+wai7hmzssbR3hWQAw0OKvRPaOIC1UQaZErBUT05RWV9EGAoK5gfrqoICLRQAVCmBKodv6A9w30b+XRH3CZjxtVMC+ffm3Vf5nSj/UGbh/+clbaimuj7NIZ3B/ilA3+/fluYpzS6q9nntJXD3tv3kLd/idzNZnVm6JxUYC5IKaiioEaXlvevktgD/trIfBZC3VXD/9Zb+dNz/PKz/Nmv+xur+O2kb/WP6Fg7dJv4/rADagYkM4By0cvASRm4/RRVQ0QJ9Yf0jI9S6ontNMV64CFdXYbSA3jlJsj5maXeThcuw8rpw+X2g+2a2Icr4EMTNNjJNkoBSmnGakJe0sPRTLCPY9wPk59HFwvCZTlC6XFTPPA0/LBTCWYALDQUifYp+5oFQlgnjo3ztKo4/dBiH0jRDuJ7SdL3pHL3VgB/O/Ksyc8P+VeGbri0L+wV0jjlXEMXjMnm9bZekGIZyag3pODHKYWyjeizHr/YUaiR0tgU15M6mffaT9LVf6qc8jsm4/2i/Ftb/LLH/ofO3dL6Kcg/+mJron9iMIhb/7yuAoh6Q59ismQE4WsjNAARQkRlAelgzXs1gpGD1JeSlxwHYPHKaJHud/mAHGWhWX1ZsPJKZbGA/Cghl/Qn2zXDD1kKGzmsCpRRY3IoGsvui6wT4VFgA8OFMwO/jJ4r5IaJ+7aD8O6N6RuCPBSYBtE0EUOw8s8i0ymRah29bCz/sPwvol7ZzgFcT+33e3j+mieYJQzld8pb7r1NL84wVpKAGxuLv7IIa0NqTe0uDv/91+dRPW6lSADGZpuDbtNx/eUzxxK9pZVJZzJ/+Mcf5MwpHCxmQT3LLuaCAwvh/I5MZwDnoi60B5IWAai15AlemBJWRh4TqTCMpHL/wPJfuegSAq8fuZXnzMiubl1i4rNkcFysaaXE0EJCZxWG0BWoRIaWY1Wix2chu1JYGSrWAMjOajrOewy+khgpSNaGfPrC3VQIT/YlFCsWVQVUoqC9VQQzXazbQxr9Qde15gL5/3DSg7/7HwjernLqlhdaDfn4ggnP0ag1Z6kI5rcXvOXdlJCQDIdmDZM/Uv2r7Nd3S4B9KlQLwQX7apK95cv+xrN9pQH4/mb/5OeZM/+ThpFDKBp6o/6OL56IExlky4QBWFuAzLZARDQEFSDNTjVMSR9fYH6Jy/LygdMaRi6+yfuIsANurx0BrFvcumYgHbX4IYHIJMq1BmVXEisxfMzajkMoKy6eBnIgX+qm0AYoYFeSHhfr7HBXknl9T6KcftFXuW+4fKgJ711FlUG/UxGcIN0KaFEuVn60t2IfXmTa0sw3o+xSPA30oF2rzQT+kefJkLi+UU2shs6CvR4VjV8ZCsiskQ6F3DWQM42VI++69b5bbCvx9mSXpa6oY/Cm4/1lLPrdRDHWx/zHr/3rSP/62oXjKCWAxB3AeuWKvnScmTTkDMME/AnYt4OFhTW99l+WNS2yvHQdge+04kmlO//4lxktw7V3C7l0Ulr/vCMb4BFxNIEl0PvUWKdNA+bvgZgB2RgA1DmGopIKqZgLuOVVH/fizseoZAZTBLaSH/HfDl+tJ+7Q5f7lvO7B3Ugf6TdSO378N6Lv+Md5fe8dXWfu5EtBCOWNX5SveucWLcseuLWzoHLsyEjq7QjIwwJ/1YLykyXpM+ogq5JYH/zrqpk3kTxvuP+b4nVWm5f6bnL9V5w+dv35/3/qvo39KSWEt6B8gP29V/Z9YApgL+XT8v9uOhYDmawBbH4DKlUFB+6gENp4YceQ/9FjcvcRgYYlxbwmArcMnkFSzsnmZw89Cd0PYeIi8JIMWmz0sJkLClYJwZSGKZSAnaSBzW7YUtLf8o2WkKqmgSos7sPD3owQmjiGuCMrnqfA/VYSLXC/ap8lIiv02YzPfKis/PMd+Qd/1Kzt6pWTtx4A/Dfo6i98Bfw76qVUOjuZJPZpnbMA/GQidbUiGMF4yFn/ah6yrW8d63vLg31am4ffrpIr7b7LuZ+X+5y2x0g9ximqyFIX7XEX/uO3CWi2UZ7gAzOSCMO0cwJkuqoAmPug7zj/J0JmQLikuf9OQ7lsJyeYbpLsPopWZ724eO4nuCCsbl1m8oOlsCVfeC3TLMwCU4VNNVJDJA3D6ipp8AHPP5n1rNQuoCwt1faC1EnDPfFIxlx2/E0UBG5SBkyYwzo9riClse57SMTVG2LSAH56vDvT9vlUUT9gnRvP4bWE0T1imwbf488Js2psBxCz+sdDZMRZ/MoCsa8G/p8n62lS+vVMsfwg5/WrHbxX3X2qfkfv35Xpx//sN/WxT+A3I6R+fCqpe+cs+QZ/vL4WDZvY69kdhAaaLcZC6bacADP9ZHwKaaYEkzX88tnpDUQbC/VfC6BRwaI8jf/gm6zYBDGDr0AnSRFjZvkRnCCc+J2ye1ezdZbj/TAuiNLoDojVaZ2RZQpJYrj/JrA8is6GnSakshM/xO063ozKTaFYXFoqGBiXg+1Qa/QIwUctl0j+Q76m9bltpmjlMXnW6C1T5s2LXqwN7/1xN3H8bS9+114G+9sHfUwJVoK81BcefKtA2lDNVMBLIBDVQyBg6O4IaCP1rQAbDQ5D1YbSs0V1NtpAZC+ROAv9Q2iR9zUuuJ/dfV/RtPwoATcn6r/MFTHwO6B//OfgKwNxv2QFcFHyD8hKQ5BVBCyu1UAhQPwNQ3nH5DEBrEwWUaPQCLO5usLd5ld3Vw0g6RicddleOo3TK0u5VRMPqq5AuwmgNEFsCyFsXwGUER2kgZSKWUjsjcGPzLf+QCvKhNleaLWYCzifgvo8C4OI8f/hjLx8zOTMo2uMzBCdVJVHmRZE2hVxX8v6xGUCDhR8eNwvou/9tuf2C3jHnyiN6KKz9iYxdLWhn8acFzaNGBvyTPTP+8ZLl+LuQ9TMDhIk2f+802icm80j6mvnaLbj/2JjmtRjMtPRPU+lnX3z+v9hulwHsO4CByhDQ/Hi7DnCmbUE4zAxAa0GLtv9h49GMtecvMFxYQouwvPEmWyun2F49hZaEpZ3LoGHxgjBe9ukfZTPKigJ0dTRQoixk20VhfP7fn2E6h655pwLJaZ79KQH3HJvzAEKDpJ0DeF75MG2kbhbRBPYwvcM3BPtyW3XoJjRTPK6/P3P1LX6/TIOfsatdPf6xtfiHxuJP9kANhO4WSKoZHhLD71uOX3fNbJZOlkfItZHbBvzbOn6r+rVx/JbPOT/uv03J55jcSPonXPjd7TeAHtA/UGQAaxf3Pp0DuOOs+oYQ0IJ7dz+wjDRTplqnc7Rmws7XAKI59OobXDl1P6PeMscvfZXN1bvYWTnOuNtndeMCySBFhsbaR4mJKlJm6TtRGp2oKA2klbZVQd2SlHZb7H8K6961mbsuK4F8BmDfK58OcuGhvk9F+edxFl3p9+2DXBnAS1nEvlTiw/x9UG2lzpncxuHbJqQzDvT19I77HLP0YRL0HcVjPtfTPC5+P8/YHRmLX4YmGMEP5Uz2NGlfGK8Ko1Vr8S9m6ERDN4NEo7qZjWCrfJQluW3AH9pz/22O92W/q32Z/dXcv79/5oJw15n+aR0KKjFH46QDuI0C8K9fFQLqzuv4dr8QnLb8uhloxs5jmr2TWyw9c5GdlZP0htusbl6gM95je+Uk60fP0lPnWXxrQG/DDGDvBOzepcHOJrDPLaSBDPcvuNpAuS/ARgSluvgPGO7fUwK1UUFuP0XyV8xaz9v8XTrss5/on3rUuBEZvm1DOc0520X3TAv67n9o6fvtVRRP8Z9SbZ6ypW9onjBjl9Sr0eM5djs7mqwjjFYg7RvHbtbBOHcTjXSM5e+q4raV2wr820qV49eX/VA/03D/s5Z9mFdBuDr6p2qWAkwoH98XEIsACheAMfcQyQD2tvOkKI8ycqDfIVgHIDMFrROl0dpw/hmTPoD0SMbOhy6gnl5ma+Uk3dEuS7tX6Yx32Vw7wx73sbT1Nmq4gQBL5xXda7DxNUCi0SjrNJukgVxYqCsW56inPCLIUkFQ4LMfFeTutzY0FPKZV5ukrDgt1KwI3PdjxhG/xmQU0PxooKbfWFunb5XDNwb4/uc60Hf/q0C/tE2Z4snDN7VXqC1fccuL5skMt+/TPC6UMxkYBdDdMhb/eEFIFw3HrzuQ9WxUT8dY/K78uajMKIA7hfNPENKKeWpbx+9+sn59uR6hn9Os+DVv+mci4qeG/vF9AW0SwHwAA/OiZVroqpRUS75dRMwAWuV00DhT0SQwrA8AzA8NiiggrYr/6aOvwvOPcvXI3azuvMro8C5J72XUtTPsLN/FuLPEytZbiIbutqZ7VRgdwvgBKmgg52tQKstpINHSigpy9xEqAZclHNJBUPhDfErIl0payO3D356MAIqd05dK2mgOMouzty6yZ2JfAOb+OZsAP+zjt48jNI/5X6Z4fND3uf08mseGcObx+6mQ7Akygt6G0NkFGWvGS2KienqadNGAvrY0j3QN6CeJoXuSJMvXsW4jtzz4h3K9uP8qabVmbwP9k1+7pXLIz1s3M2ipAEzfbCb6pyr+vy4BrNguZwC79nAGUJSJaDcDyFfe0iYPwDgJTAkHrc3iL1kmqIUR2T2vk71+P1fvOwqHL7H0esbixhvsLh5ld/EY1w71Wd18A5WN6G4J4yUxzLyNAspLQVsayMGCXxtIcqDGFKYTu6ENReSkSQnYO4lLMCNo8wb7swIzvknaMpwdlPfVRwLNS/br6G1r4fvHVkX4TGPpN1E8pXh9vzaP9mgerxRzXq5hgFmlTsPgiHHspgsO9LXh+DvaWPqJNhy/KhZDUiq7cZy/iNwL/FPgLsxb+Qmt9T8M+nwL8KvAy7bpl7XWf7vtNeqs/1lk3tx/k8S4//i4Jq3/tpm/ldcOSj/4CgChlv7xwz9L9IL3LGL0T1UF0EyrUkhoedt9v+UksAwaooAqfAA6g2NXyTavIFdOoJe2yPoDtNIs7V6hM95ja+Vurh26j5WtN8jULpJi0FuR0z8aGw2EjfzJxBbOUnaKTeHGyC1xU9/IrR9cKhFB4VbN30H76KdVAuF6v7HP+XaE54+9x1WRQNdbqn5TdWBft70f0Hf/q2L2y//jFE+5GqdRAmE0T56xOxDUSOhuQmdXoxWMloTRsrH4XfKWdjRPJ8sBX1SWByUoldmZ2o2jfcbA39Baf15EVoHPicjvaK2fDvp9Smv93XO4XmvH7+3G/bcZ17ylDf2TWpAm8tmMtTr+H8yzLMJJ6x3ARryF4PNeltu34GThOOoDcGv1Kq3R97yB3lmGC/cwuOcFls6BRtMb7XDo2mtsrJ1hc/VepHMBNd4074vCywOw/7FlIVA2jtooH7GfzYLxFoy9sFDfEez+51Y/NvvT+T5mVAINvSckpgzsHTYaNrM6fdsYTFW/tzrAn9xXpnb8PrOAfp21H4vkyYFee9E8qQF7bUE/t/gHCpWSO3Z718w7sHessPhdKGfM4leW5nE8f2LpxraosW/w11q/CbxpP2+KyDPAGSAE/+sm+036mna1r1sx9BMoFH4QholQaf3PQv/4CiC3Y4MFYKoygCcBP64AOqT4C8HnCkHZjOBMVfoA8jlEpqA3Ijv7KtlXH4Yrp7n6+BusfbVDMtAoPWR571U2186gt0+TjS6xtHOZzh4gwnANdk6n0BWzSLzSZpF5pY01YUE7XxQ+MROHzHH+1hdgIngKqsf3B5hnXiwe47bNLMrw9qFfIP9feh+TXEG6jOiwqqiTcDtvJ95e6lMB4vm1ZzRYKi3/Rku/Guz9zz7g+/3r6B237YO+e8eqQD+neMCUZ9AUSVs56BdlGtQQFi5rkqGhecYLFKGcCy6UU+cWv0osteNx/G4d7I7LTr9RtI8vInI/8CTwmcjurxeRLwLngR/XWj/VeD7v8zyon2kLvk19/pbcf9UxVftKRdsqFEDjdfZJ/4Sc/7QzgDJdNN0MwCVS+TMAVJb7AAxbo3MfQJop6/gy/LysbaHvfhP95mn0yiZX338NtSMmHFNlMH4NLt+FHhxnqHt0eAvRmt41TTJI2HrArjFs3QHGB2B0WybGv+KoIBEs7yq4sFBj8TMxE3BJYjE6KAfotrMBys/OL+ncFDVUfNftKM0qxVElraz+1uAfRPu0jO4J4/TdvnChlSZLvxTi6dE8OcWjrTNXg04LS9/E7yskX3zFRPN0ts36FMNVYbha0DxZh3LyltKoxBgOzuJ3dI8rP+7eJ2mJk3MDfxFZAX4J+FGt9Uaw+/PAWa31loh8F/CvgIcrzvNx4OMA95wpF6b2FcB+Hb91cqtw//4155X5WyVN9E8xtknKoK0D2M8Adu3OARwqgJwa0WWfgLZJYWNU7gMwJyv7AMiUOZ02tJC66wLpxhpcOI0sb5Mtjc0lx8Za73EBNRyx1z3OZrLA8u4bJHpEMjCF4carlmURzBTeagIH+o4KklwJ6OK/4/6zomSESJERrOz75tNBUFYC+TMIZgOV4n9FkUzead/d4ntsB+YxaTou6uCtAPvwmCbAD/u2AX0oZpPOoRuL5MkpHsgrcebRPBnFiltDQY0Lmqd/RSMZ7J6wNM+SJksoQjltuYac5lFZ2bnrwN5GmrkZQFuZC/iLSBcD/L+gtf7lcL+vDLTWvyEi/0hEjmutL0X6fgL4BMCT7+3V3sl+uf9Se0vuf5oFX+L7J6kWH+CBuWT+AlH6x2zHk79i9X5ii7+Uir4FCWBVGcDhIvDuybtFYMIZgAv57KiUTAtjkhL4+HWBwkzgXOk4uiRTgEI99BKjpx6HN+5FHnjRJmKZH2qSJvSH66h0xM7iaTaXH6A72mBp+CbJjvlxijL0j040aBNhZBSVDfOxVFARFqrz7GBHBQkY5YSQWHNevB9xSAcBeehokyKodP5SPl9mV/uYjOMn/+5jMivoN0k0rHMKR6//uQ7w3f7MA3f3BIpSDPWWvuPzXcy+zjxe36d4fNB33L5dY3fhkqYz0OweU6bW1Kqx9NMFw+vrbgbKhnI6i19lJNbyTxID8s7i77oZQP4etXvu84j2EeDngWe01v+gos9dwFtaay0iH8Lg7uU251ciZFNm8s4q0zp/58X9113b3zdN5m/zvcb5/6p6/+H1wgggPwFsmhmA36dpBuCfE+twjWUCK4wjONOaLE1MXL4GWRiSnX2N9KUH4eIp5NQFE7YpxurS1zS9dIt0eIVB7yij7hrXumt0kudJds0aqSCMVzJTHE5JERGkzDhEcu8ExUwAWyhOgtXBbJQGUksHAQboJWLxi7c/591bShVItJxhzqukc+y31TaqR3vtVU7ekM8Hzy/UQO9UWfo6oHtKFI+2a0UMBUkhGRirv7tpckpUCoNDitGqydhN+yZ5S/cMBUvHhnB6jl0XzeMs/kRleV6Je1+KpMl2Mg/L/yPAXwS+LCJfsG1/E7gPQGv9c8D3A/+ViIyBXeBjWs+G6PNO+roZ3P8s9E8xrvlk/jZJyZkcKINKzr8hA7h8z0kO9lmoTGRyHYCwEBw4NTHpA3AzALMoTLEimNbQObaO3rhE9vZJWNtAFnZBYHg8ZeEtBalmcXiJ7niLraX7ABjvPMLy4BUSPQCgt6EYXdPsntHFknmOCrKlIFDG+ec7fv3QUBGdh4LmZSA8OqhSCZjDo8lhoX/APaOppcVr7/sU6qSNAzhO99SDf2jh+30maJ+WoA/kS4a60M2JmP3MgHsRvhmheDJyx66z+Dt7sHjRgPvOKUXah/GyzUvpafyqnJKUQzldNI8P/D7X7yx+R/vcMM5fa/0HNLwuWuufAX5m1mvMav3Pk/tvE/nTPJ7pnLPmus2Zv+H522b+ton+qTp3ON5YBdAmBzAQDQH1q4L6Wa/5cb5BrIvtcAZg6BVFps0avaYKKHTPvsZgcwX96lnkkechSdELis3HRyy90qGzCYneZUG9wF72LgC2+/fTH12in15BgO42jNdhdMgCiuX6tS0FobVGlGG7bJl/wGUjFwlimiI/QNspuxaJKoFUS+kJT+QL5Nt+ETjvWYezhhmlKlQ0JrM6e6vAHtoDfqk96BNy+n5JBqAUxQOQphb0tf3vwjedxW/r8pjYfUw0z56gBtBf1/S2TLbuaNnU6Ml62vyVHLvNFr8SXWnx3wzL/4ZLW8dvKFV923D/k2Noz/1HF3Wp4f4hHvuf94skfgFR+mcWBVBQCYHFH4aW2j4h/eOeakj/mP5FCKjLADYyGQGULwRPEf44NkY1Y6zJnRdaKxLDwhmA2Z/mwKCURj/0EsNnHoM3zqDuf4VMQC8LW18zMj/mkQKd0rnyDOm1xwAYdI8z7BxiaXiejh6weNGsD8BQQGvzuVOEhZIYQNeJBfXMcvdKvJmAzsND3fidT8D8uO0swT4Dcd9jhF7L77eO8/eMmXBm6y9A40sIKPvl/quO1zEl0BDCWQf2Yb8yBVRN70C9pY+2Mfva0DyS+RSPieRRQwv6m5q0K+wdUQwPmxW3TJkGyHr2ZbYcv+pkxlhIUuNCyuP4TfKWUuY3UWXxd+xvr+23c1uCfyhtHb++VCV9wfy5/yaZR02g6yWTyiQeAeQngMUygMvPyMsBKDmM4zOA/BrgAbwO3vJJH4DpWCiHNDOzuQzoHtoiu+cc49fvhfUN1JF1tNj3SEDrzCiBjnBo9zm2eveQJsto6bLdP0t3vEF/cImFt0eoEThyf3BUMzyemVvTGL+ADQVVibm1cCbgFEBhytt3wYaIipjTZDDB/fszgnym5D23Kms/FtNfVRZmJuqoQmIA78Yz0RYB+/AcdaDvK4Ym0K+kd3xLX2NKM2QYmkeT1+XxKR5XiXPp7YzRsmLvuAkYGC8ZSz+neWw1TpexK4m13oNyDS55K/FpH0xQhG/9u89t4ee2Af9pqJ/9Fnwr97l53H/dgu9trrtf+qfKH9E2AcyP/089y7xNCKg/AwjLQBiQ8yOHjIQ+APcDd5QKNg9AtKkS2jvzJtnVQ6Sv30OyvIXqD80ZROeO4PGaOevK6A32siMMuifopFuMkhVGS6t003X6XEFsVFP/CmRdExpqEN+ey3cIKzGhoVqbRDFV0EFm7O6GCp+Jo4SUeFQQZXCPKgLvdE20T2WSlzdb2I9MkwtQyfHHrH9vO+znO3GL7TjoA9aha6N4wKvHU9A7ZCZJi8xE8kiKoXg8a7+7rdm6O2G8hKF5utaxm9TQPLYuTwj8zuJ3AC9QAnsTHuwpgRsd538jxFcA0yR97bfg27Tc/7xCP82125d9LlfcnJ8CKC3uQhHFESaAuT6lYnBuzFPUAMq/EU8BgFEAYztGs3pWyjgzIaBhJnAm5WQefwZgXqHMLOL+yIvsfOEJslfvp/Poc6gkNat7iVkoXithvJTR2VEsjNdZGK+bc2Yd9haOMlJHGKlD9LIr9LJ1RAv9K6qI1bbhoVj6RyuQxDiGtYrTQROL1tupgv+jD2khKNM+MEl95M/eig6A3qeLfMmV9pQz2iqJXSOcEVRG94TblZx/Ae5ufwj4ZZqnwdK3dI+4dXWHxtJPdgvQ72+Y0Q3WhJ1TJpon62pTmC3BLLcoTNI8XsauC+UUPHqnwuLvqAzFzY32uWkyK/dfJXXcf5vEr8bzzzn0szz22Qq/Qb1/ofKYlg7gqhLQeU6AFKDddgaQ76MmCsge59YExp0mLwdhHMHdhQEL73qJveceQb95N+rMebRVWo4G2nlozNoXe6C1LS2hSdSIfvYW3ewqg+Q4w+QEY7XKwvgCkg5QIxtBojAg4t+mnQlgKfiQDipqBjkxB4cOYiCnhaBwFFeFhYZO4wmfTLhtxX0f+3UWV1I+NcCvI+0h7RMCvuvjAN9ttwF9nVEkafmWfmot/aGjeUCNhN6mydJdPTdmcChh+26VL7E4ttU4s57NDUkKmgehoHmSwuL3c0GcY9dx+kUcf2HtTzh9p5id3dbgXyf7LfhWJ/Pm/q9X5u80ZZ/9cVTRP1X8v78ATKwCaCwD2FcAdTOAvGaNNwPIk518aiPwATgFYDhQnVMolmjK4+u1aPrHrzBef5vxm3fRPbSBWt0yiVpuprCo2XhySO9CQvea+XEPjmiW3lAkeshSep5RtsIgOclO5z466jIMr9DdFuMPUMJoRZOuuAQx06btYtshHWRonkIJuP9+roBTAu55Gkdw4R/Igb+G/y+1e+9NKXzUl4oZRJ00OYcn6J2KfXUWvr8dgr6jc1qBvqN3tAN9TBSPq8DpZ+lum8XUV86n9DYzrt3fMdE8rkRDAtmCne21oHlcVI9v8Zf4fIrvuWNLhceAX0n7+dktD/7T0DvzsP7L155PZc1Zav6Ujo+EfsakzvqfF//fZrGZWR3AuXKwYN8mCcztq/IBdMjIkMYZwNKDr7C5scr4pQfoP/EVkkSTZSDaOOd0P2Nwr2bvbpVbhHsnMhYuKkQLXb1FMt5hLznFWJ9ANlboyAWUjCCD3lUYD4XRkczkBmj7pyxwKZcPMKkEJP+bVALY0+Tholo8+sfcr3YrkrVUBm6fk9i3vZ+In9ivuQ3HHwP8CaUQtntg7yz/GOjjrH1L9zjQN8XYKGieHSEZmSzdxSspoyXFtfs7DI4IWQ/GbsEVy+2bapwmqkc6LnTTi9uPVOWc1eJX4so73EGcf4neCRy/Nyrpy/S7+dx/bP9+C79NG/9fKvngcf3NFUDN1XwFkEtQBbRNGYgmH4BrT9CgDECIlngoaHfM8qNfZetL72b08v30Hn4RpSC1gJqh0AoyyQxdM1aMjgtZX9O/rJCRkPZTWH2DZGONdHiKgT5Ll8t0WEdESHY0aVdBx1RtpGsd0SZ1wWMAACAASURBVIk2AJ1YsFeFjwDMtoBdn1Xy1Zrcfz9cNN92TzufWRR+AjNbKx69UwCpd4wv88gNcBIN54wAvGmfPC7k8F1bsX+S4nEO3KIvXvE1lYO9T+/IuGzpu4VWlt7KWHprxPbdPTZPdxgexoC+R/GQMEHzlKJ5LM2T1+F3fw2hnCHwuxlAR8w3V8wI2n0XtwX4h1IX+VML3rRL+ppX3H+V7Jf7r3P+1o2tyvr3z9mm+mfTfVVx/kW/2WcA0/oA8hj4imSwxM8TOLTF+Ozr7L1yluzSVTonL+EKw5VoIGNeopUmPSTsLBuL2kWA9Dc36ckuQ32KkT7BiBN0uESnd5nuHuYGBLNYRx9jgarCv6ETzC/YRgM534DYu8pse0EHeeGiRGYFkFv87hhn7LjZgHlWpm2C448A9n5pn0kHb3x/zLJ37VWAD4XF76J2qAN9z9LPQd/SPMmuoe4Wrmj6VzO6Oxlb9/RMMbaeV4ytbymenv3OFHk1zrY0T+jYLVn2MYs/ePen+V7gNgX/UGYt9zwL97+ftX7nFfpprt1+zd/y2KoVQBtp4v9LfX3Ov8IBXBcC6i8E729X+QCKY5moBZSJzp3AZocpBzH2SiwgmqV732C8fpjBy2fprG2i+kPcIi5ZZp+7Fkgyh8jmzcuK/1lXo0ZjepxnVz8EJIz1ccaD4/QXXkDE1BrqbkE6FHRXk/ZBd+34mpSAogBzxC4w71NC1YoAyr4C7QG9//77SqH47ovPs4Q/hwAPZSUQi9/Xwb4Y4Je3sUBvo3sc2GeO5pEJ0H909Tz/4pt/jZXEnOv8bpfv/mc/zHjYp7cB3S3NsS9eY+vBVa4+1GW8COMl8z2bqC6P4rHWvovmwYG9y9JtoHmAHPirLP7irzBfS/1afh8yY4mdGyJPvrenP/lvTuXbPsCHln8I/r5V7zt+Q+ontP79H0DpHN4jDV98pwBC8MtTyIN2t+2De+n8VgFU7rftzvqP7Svt1+V+Wb7tnd9ZWBPHuLFIsF11zmDbS+IKP7vzpp4z2L+Oqcni7tWk3mfecX5bfjxFFUZ3fNimtTB24/PXXrXbo70+Vz/7PtTCgMV3P41ZxMVY/KlbrCOrTvWXXWHxzSQH2TFLDLN78KW3+LwBWBG0VWajJQ0dSxkoctqHxLMmRVtayNJDFP+dopOADio+u/aizUnpM2Vpsib9Y6sienypc/LGQD5sd0Cf7/fAfsLCt6BPRuHI1SCpsCADfvwDv84P33sJhdhcCzNLHOmMj/71v0Z/PWX7dJedkypP1NI2UavE64eRPB7IT0vzhI7dRDLCGYAK2oA8w/e3/tKvcPmZS41fxG1r+V+PpK/ac5T49+nCPiszhudE/7QuC1FB//j3NKsDuD5KqXkG4K8CNusMwB1bBqtmR3AiGqwSENH0FvdYefQFNp96jNG5Myycfd1zEGemtjtmdqEzZUI1xcwOtNLoRcXgZErvYmIwW7bpdZ9jOHg4H+dw9xFUskmn/yZi3+XOrqCVcdDqnjaUkHLgKMailCJKiEzyGYEJazXbklpr3uOADa5JPjNw7U7E2wiVQpWVn7dWUTvR1kkFUbb+y21Ry95eMwT8HOzxQN9Z+FkB+mvdHf6zJz7DN9z1Vd7bH6DoISIMxglbwwWOLW3TRfFjP/g7/J1P/hnSBRgvQ9axM7REB6BPmeKxz7iozVMkbVXRPEAJ+ENapwr4gVJ45x0T7SPBbdQ6d6egfmbh/tvKtAogfo729E+b87ehf6aROgVQVQG0dO2KENBibJpoCChEwT6sDmp6+EqgIhtYF+sGaPdjshzx4onLDO++wODcabpH1knWtsy7oEBcHoAGLRlZqsxLhaGCNBnpmrC7pE3Nl7HQu6pYWHyBNF1kNLzXjCFdZbiziupeRi2sI5IiiMHzAZCC7tvB5jQQFuytn8DRQlAkjVmw136GMFZR4FNBEiiASaUQ9intaZgRVM0CfJstRvtMKgByBRMFfG0B3qd1gv8yFhQp3/bgU3z0XU+xqvZYUCOWJOHq3jIf+N//bj6Ol370xwD4pidfZfhFTK19u4h61sU45m1phtziz3l9G6vv0ztevX2f5nFA72ietqGcIcVJfrxbwL2d3NLg3yR1kT/TAHdb7r/K+m/D/Vedp8q6n1fmL9AY/TNt+GeTTMwwIhnAsRBQs9+7lyAJLAf3XAGYFziz3LuvFJxlX4h5Sm5RmHGmcPH/ylIqmZZcGYjKOPzIC1y6usbOcw+z+v4vknRSlPbKA1vgcbH4Jt/SRO6YMtKC7hg6KB0IyS6oZJfe4vMMdx/GaaNsdIxsdAzpbqB6V5FkDxETZaIz0B1j9etEDAYm2iqDAvQNgphoIRzdI7af/Z+DuBS8sFhfh92KKgPzufFrbyXVwO8+BCBv20pAD4Zmc0ohBvZ2QRWVwje+61k+cN/LLHUHLMiIrmT0VMrW3jL/6AvfyP/66T+bj+NbHyhWl10f9hitGgs/63lUXClm3+P1PYqnFNJZQ/PAZI2eplDO0OHbUcaUTby2NnJbg3+TlEG9XcG32a81uwJoPPc+Cr/V9YvPKuZD/zRlAMdCQOtmAD4F5EcBFf0oKYVychi2rShv7DuCzdV1rhTy0SYZh772Wa587n3svvAQK489l6sX7dYJyK1Uc22tjZoRbUeiNFoUo2Njsi1Fsq2QVOgtP49Olxjt3ZuPT4/WSEdrSLKH6l9Bkk1UZs+TCJIZINepFC+3PyOw2zlV5GoIWTrIPd7S7EB7MwLcpMIqFW+24GQWJTDxs4tZ+8G+CbB3lr0DfPfahKCfmpnQyeUN7j68zkceep613h4i0JUUJZorm4f5zWe+jd9/+usZjPsAvPvk6/zKx36aRBXlNf7qv/se0r4uLH0xoI+Q19yXxFruHsXjfC1T0zwWvMP9VcDvW/7TAj/cBuDvbFsn+1nIfR5x/zeD+2+StoXf5kX/zKIAoJwBXBcCChCuAxAqAHM/5e360FAnNaGgbtvOCAAW1rZYffAVNl98kNFbJ+jdddHMNi3vn3P92v2319BS3lZCupaRrmgYCr0rCcIOvcXnGO49iAn1AdVbJxsvk+6cBjVEda9Af8Na6CZSR1LQKQXY56BvE7xcWI7zEeQKgEplAHjb7oMuAbVTDqG0dfiWjg0oHrezEux10ZaDvX20ogXJMk6ubdKXMe+57zVOHr7GQjJiJRnk13n5zbN85un/iOdefwSADz/0eb7//b/JN506x3G1kPfTwL987R7OjY4Uq2t59A52aUWXiFdy7nq19puieULgd6XZfVqnzuI3fbIc+HOHf0vq55YH/ybZzzKPtxL3P6/Qz9j+knJokfzVZP3PKuESkK3yAZxEfADmOKMAHN3jzwAmHcNGYjMA3JrBEUfwyn3nGFw5wuYLD3L08AbJ4h5gq4NqKTmDfZ5a2e3MNaBynn54UpNsKXpXFP3ey4yTBRBBdXZR+iJ6tEw6OEo2uAuGx5GldWTxqnHiugmTBhLjG9PY+7bJYoi9pNgdltqCCmUAuZUfKgXsKcJfWa40IoAf/UnGKJ8Juoc42AefxVr6i8mI0ycu88T95xCBpWSP5e4QEehJyvrGYf6PX/6r+XWXFrb5lvd8io889h+4e+0SyzLgq6MOr8kup5Tw5s4af+Hf/iDDpA89nYdtkugJh26xyhZeDL8Xo+/RPNg2H/hdeycC+kAU+Mv9sgmLv2lpTV9uC/Bvsv7rqn3Oi/uvSvyaF/df1b6fzF9/f1Q5TFjq1kJv4P+BgoufWBy+4PbD7XAJyJgCKEA8PgMIC8GVFQDknIdAImkRHurNAMz3oS3YU/rOMvtc/EelRDj2+LNc+MwH2XjmEY6+/4t2v02asqUDUsv1K1WUCc4yE0JofACGFtJKoCOkHQ1XbNkA2UP3MMCGRrpb6IUtyBbJdo+it0+gt0+YR7J4BVYuIp3insQB5BDoGmB3ARO5Y1hRBn57YP5q5srAfgUl8J+kf5pMrjq6pwB9ClD3t+1nyWkd056Q0euMGQ8S3vfYK9x18goLKs0V0WJnxGDY55XXHuSTf/TR0uXXlq/x3/65n6XXGdOVlN2syx4d1rdX+PXnnuSLF+9DdwDr1M0tfSlAX6nMWPwVoJ/k/H3hsA2Ttqbh96HI3C3KNrsQ0LLF75RBW97gtgD/aaVtyYfrIfsp+zDPzN+29M80C7/PUv0zNv55zwCAqA+gapGYskxGAkGEBloccOzx57j0pXez/fJZVh56JbfqE8UEFeRmAiKmvLTWYqKCciVpZgK7949YfK1LMgQ9MuMbL2vGq9oUE9M7JP1d9GiBbP2sOXT3KOweNbdz5A3obyF2jWL65M/D/QRkaBy52s0SnIPYzhScQzifJUBJCZhtb0N0e+K1CvBj+7ShcHyw73dGLC4NGe52OHPqCveduYTWQj8Z0k0KgByPO7z26gOcf+0sb751Gu29Qw+cfok/96f/Fd3OmJSEkYaNvUVeunSKf//aI1zYPmQ4fQf64ln6SpvlOKWI4ikieIr2kOIBvDV1ZwP+UjRPA8c/baQP3KHgH0qd9T/rYi9tuP95yfWkf2qvG1j/sTHNwwHsJAwBBagrA2Ek7gMoO4FNP6cASlFGbl8YCuqsLhc1pDKWT11k78x5tl67l/7RdfpHryJaSDNFYqkmty2WZok5hIufrfEF7D00goEJCc06FJawAgaGv5HuHsnJ59DDRbKr9+Xj1OtnzP/uLvT2zF93D7oDg9faWP66p4tf+8goBGOekvsACoUAOT2E9wzz5zPDux4Afw7y+VdgzikZ9PtD1o5sc/zYJsvLQ7IMFjtDFpIxys64usrkW7z+6oP8yR9/Q36ZQ2vrvPdrP8+D973E8WNvs6hGKDKUuGcvPH3xDL/0hQ8V0Tuu6qajd4Q8isfVVQodun75ZZ/ikQDkhcJyD2meOseua4f2Fr/r21ZuG/CfhvppktD6nwf3P6+ib/sN/WzaPw/6B2C/EUC5RGiipjIQpl/ZCTyZB2C+ifwVyduLGYevBNzawBnm+i7kM6eB7LWOPPpV9tYPcfWZRzn14c+a8M8ktd+rAmvNaS15WKijfQr6x6wn7EJCs0wgAZ2ZwnPaLSSiBJ0IaleR10bo7aBOPIumi774IIWlnsHOGmwfsdspemEbFjdhbdM6f+2z6GrjyHS00cj5EAT2lKFaEpPBSireNeyjnwL7JQB9Y91rkiRl9fAuSaLZubbAYLcPGk6cXuf4fVfpJGO6ObUCC50xaMW1K4f4zO9+e/RaH/223+DY8bc41N011JkIm6M+iWiubK6wsbfEH792P+t7y9AvLHwUeTG9EqfvWfoh6OdgG4B+zKlbAvkKax+KkM2wPYzhr1IGpm+GtFQAtw34Q7MC8OVGc/9t5UaEfl4v+qfNesFtFUDt/U0xA6gLA3V0T97f6+eug4RZwfU0UK875uR7nuL8Zz7I1Wce4egTTwP2eOf4tRa/WzO4qCBqlINbKtA5gvPUNDHbLhZT2+1MaQPCqY3ESUGlI+Tu5wy9oQUS+7anXRgtwmAJdldgdw2uaFjchoUd6O/BoQ0zFMGgfsfj71fG5tkkHnBfU2apycUUxkK60YOxoFbGSJKR7nXQQ0VnZUT/8ABJNKONDh2VsXBoQDZW7FxcYrTVZ/HwDsfOrrOwMM6f7dHTwt5Oj92tLsfvvoZS0FVGgW5cPMbVt0+yu36IzatHyLJk4n156OFneOzxL7G4uIuIsD5cYrjb5crVFTb2Fnn+rbsZ6I6huxQG8K1TPOf0K+gdP3SzVF/fo3lgkuJxbfjbElj6nrWfv/ul9rJlHyvkFgL/NDIX8BeR7wT+IcaI/sda678X7O8D/xT4AHAZ+PNa61fmcW1fZi33fD2kyvovjaGivY31fyPon1mqf/rH1SkAvBc1FgIac57HCsHFnkllHgCUZgBAez+AnQkoDYuHNjn68Itcef5hdt88xdLpt4p+FuyxYJ9pAwIuKsieLA8NBcgkoIM8JaAzS80k2iQ2makIbBslI5KV+H06I+iOYGkDfRgY92GwCtursH7S9Llg+65dhaNXYGWrCPjxqR8xD6h70oRLijJ+eHVoSKfkJwCVapJ+Ztk4zfLajrWIza0srA0YXlpg6eQ2C71xOZJIaTod6HZ6XHn9XobbS4y2l9i8fIx03EVUytqRK9z70AscOnaZlbUNVlavspCMizFr846O0oSnXriPV946YaJ1XekNr+BaCPo+vSMTlTcLoBfiDl2f4qni9vP3kBDgs2h7/mgCLj+0+P1+pZlxC9k3+ItIAvws8O3AOeCPReTXtNZPe93+CrCutX6XiHwM+PvAn9/vtaeVm8n9zyP0s0qmoX/y87egf0zbbApgGok5gKuSwMpg75ebrvYB+Mf77bEZgDtv1Qwgw+DH4ftfY+fSMdafe5iFI9foLO2a/dqUifbLRWtdOITNBTJLA2XWF6DsTMD2d2yVBaW8ImVqL54J6UqK2lWGu7d9ccleFE26swtLu3D0bdg6BG+fKTpsHDZ/eKxMfw9Z3kZ3UuiMSBb2yJb2UAsDwIC7s3YLANck3Szf7qg0B/68R5bQO5SS7i6ys5WQDnvsXD7K7tXDDLeXyNICikSlLCxvc+T0mxy96wJrJy7R7w5ZSoZeeKliZ9Rlb6fHyvIeY51w/tJhXjh3N8Nxx5ZWpqC7VEDvNIB+mKjlAN239Ev/I9Z+jObJ90Ucu/Ow+JNKhJuUeVj+HwJe0Fq/BCAivwh8L+CD//cC/7P9/C+BnxER0S1KioYW+vVK+golVBT7XfCldO4pqZ821n9b+qdu4Re/X132b/S+p+D/gVYhoLEyEJNgb6XWBwC+w9e1h6GgSnRp4XclhsvPrBIwvgFj1YsW7n7iK7z677+OS19+nNMf/qxJ9nE8P8bidLkAot0zJW9zlUSddWxCRIulBosyEZZ2UpKHQmoNWdcoAhcZk0fMuMqVrriZA43Va8ba72rYWYJXH5z8IgcL6DSBNAGtGE/2mBSVGuWQJmTjBDK3VJn3PbeUR7/19+gv7aFE07McuAgM04Q07aMHin5/xPbOAi++doqru0sg1nHrZiK9LKd1sH4D8po7gAe4VfSOb+kDE/V4YpY+lMMyJ9oCmmcifr+FY7fcHtBKFP6GNjIP8D8DvO5tnwM+XNVHaz0WkWvAMeBSeDIR+TjwcYB7z0zye00yDfUTyjQVP9ty//Oq+T9VclhL+qepbZrqn2aM7RRA1T3MMgOo8wEAuQPZXcene6raK2kgytZXd3HAXU88zfnPv4/1Fx7k6CMv5oSSUxSJaFL33GxUUJoZgPFnAoAtG61zx3AGCMby184HAOhMk68lYGcCRhuIdRTjhUsCI8zL7bcv7cDjXzYW8bAH5+6FnWUznMeeNWNKE5JMwbCP3uszPlcuS108noRsZ8l8lozl+17PcXjr3Gl02g5mlu6+wLCj6WNmULvjhI7SjPc6bGwu8taFwwxGvXJ9o64D/UlLvy3oAxP0js/rz0LxhE5dgCaaJ+bYdVLdXgB//m62RP95gH/sUiHatuljGrX+BPAJgPe/t69heut/1pW+9tO3jcxvTeDmTNt5RP9UXbNOAVRJ2xDQOs6/OFeoXLzvOuIYLmf4VmX+NtNAeQipJ2un3mb73te59spZlo5fZunYupkdUFQMBfuylxzCkm8nWKezVy+oTglgnbFarBJQ5r92YO/0nlMSbkYwtjOBIbCQmbj2TENvCA++CJCHqAJIJwU1JFnZQQS6Zy4AlvrIFOm1VcbXDpFeXSPbNeC//MiLLN71Nv2O4fUPPfyyGYsGRkKnm9LppHRV+Zc1TBO2hn22R312hx1kN2E86HDt6jLDcScH9bzcggN8C+qubYLWsf2U2HYH5PsAfffduucVUjzunZkE92aaJ3/Ha9r9c8F0VI8v8wD/c8C93vY9wPmKPudEpAMcAq7M4dqtpC7ypy7sc+I8c+b+5xX6WXKkMrl4TFP0T1v6J6Z06vh/AJepO00OQNTiD0NCc0u9DPbGuRufAZjjYcLh67UrYSoaKNPCqceeY/fKEd7+8tdy9hs+TadnyBJ/zWBHBeG9Gzn1o4VMg9ZlOshtK6sstCqvS4uSvA/oYjFyjxryi6Dl5Y61mFnCHqATM66+AVWdKePqSDIz1kEH6aWopTR/UOOx0OlmJIev0Tl6DbesZadjePM0UwzHCb0kzcs4ZGPF5ZeO0O2POXz6GuOFEUoLg90uaccsyoPY2cLmEpvriwa5E8COJbfs3ddvwTwHe8gtfMEqMnHcvQN7S5UEC+D49I6/HbP0/f1VoA9+2Yb2NE9ze3EuB/q+MjHfUDumYx7g/8fAwyLyAPAG8DHgh4I+vwb8MPBHwPcDv9uG779RcrO4f9gf/98k09A/dVZ8E/+/nxpAbWcAbaKSQgUA4MpDlJSYrxQsjVQVIhrWBTJS9il0Oin3PPklXv7Dr+Otpx7j7vd9qYiasVdyIZ9O3AhUvr+gg3KfAOTZwm42UHwmB928xpCbEdh2Y/VrqyQoaJ98n9nWWmCYUKrHoLv55nCvi2xnqG6GToVskCBK010eIh2T7av7GYORtaSB0foyeq9Dd3FElilGex0QGA177Lx6onimAloyugtjVKIZDTt2fQTtWfSBZQ+5EoiuZuZZ+CUO337O+xGC/HSWvnl7ir7uvP7ssA3N497Jto7dWFTPLLOAfYO/5fB/BPgtjJ7+J1rrp0TkbwOf1Vr/GvDzwD8TkRcwFv/Hpr3OPKmfxmtxfbn/eUX+NIV+Qnv6JyaxGUiM/qmTOv4fmIoCCtcFsFeo9AGEY4iVg6gG+hYKAPKIoKVDG5x89HneevZr2Dh3hsP3nSuvGQwF7eOLB/ZOX7ZRAmB8BFBWCv4KV74iEMhXuTJ9fAWg8/ZcIZBRKr2MGGcumCQxYLDXs7cgsJ2h+ikpkA0Scz8dSEemWik9nT/38P4BRuOO+dGJhk6WP4twbYJ8wRn3NebbDpyrQd9RO1AP+uBZ20F7Hbef75+S5gmBvyqU0+2HMsc/K/0zlzh/rfVvAL8RtP0t7/Me8APTnjd8T/ajAJqSvma1/kOZZ+jnfjJ/YX/0D7gs3un5fyCnU+ocwKVrTzkDCBPB6nwAAGEoaAzo/XHHaKCi3VcoBRV0/MFX2L50nIvPPsLysSt0l3dI0Ljy0Y5Ccmv7upmAUEQGmXM7OsgMKEYJgbGy/TVtc/rHp4YgX9FLJzoHfvHu1aeKzLZ7dk5ZeF9U6bPt79631CqHju0YWqgS+ezAW4rPPsj7vL07zF+AxtE3PsCX28uJVznt4wG+6xejd6ax9GORPPnnGnBvKtXQRPWEbXdkhu9+ZZqs39D6n9X5O411vF9pY/23pX9K+xv4/7oaQMXYmiOA9qsAgAjdU76uf53ieEfC2CdQQQOZ85M7g8vTb9Pn3vd+iec/9Y2c/8ITPPANnwblnblhJiAUdFBiLX0zFgExlUjzWQIuwlPnoJ+HiHrUEBhaxbSTzwzcrYA3QzAmvxmHPWcM7PNztQCZicVf/Gcmrk8A9F4/Ke3XXjJamcaponV8B67ZrgZ913+/lr5/HFAJ/JPJX3HgDy370OKfVd5R4N8k02T9tuX+fWnL/c/D+Ts53unpnyb+v47bj/H/bRTAPMX3AcSSwQD8stB+RnCMBooVjAtLQ/QXd7nnPV/m1c9+gIvPP8ypx54H74oTCkDKgA7tlIDWgn8nGkgSj/6JzQDydtNmrH9zzphCKI5hYkNKzZPfXXRBEfH3l5+Bv9u37CVQEKGFP6EA7DmuB+iX2itAOgTmWWieuuStGNWTf5bpzNPbDvyvZ9LXxLW4Odx/7XVa8P9FW4UPoSX9Az6Ix5VQfq2I9d/GATxNBBAwyflPEQUUzgCK+43PAMx5KO0rKQCIzgKO3HWBrfte5fLLD7By4hLLx4vAtsw+c22jW/z28AlVKYFEKLKGoZQ0JqLzapwxRWDa8f7bNQlsH18huHM4qfpVRQ3QCqu0hPmlWUA92Lu2yf2TgO/alZRBu2ivB/28nYr2wNovtXv31EznFH2rInqgHvj3I7c8+IfgPvXxDUlf+4n7vxmhn1XHlsZZNUOYE/3jX6Mt/RNLAIPpQkBL91hDAaU5QFdTQLEZgOlLuZ2Q759UDkomZ3T3fu1TbF05yhtffIJHvukPUf2RfW72O/YsfiXlkNKc+9deiCiG4nE5AX5+gO8bAI//994njQ/+Abc/sU9P7Pf7xMTvO0H14O/TwXa53d/fBPSx42IWvusfAr7bH6Nw2lj69fubQb+qKqffp86xG1r8+dhpJ7c8+EPEut9n5M80Bd+m4f5vVOjnzaR/mhRA8SyaM4Cjz6lGAfjS5ANwCqCuHARAGArqzwKaaKD8TiMRQaqb8sD7P89zf/CNnPvyuzn7gc+jYrfszh3SQRQWv1MC4M0y3L1JQdlICfRNu7/fjTiv009MEeioUij2zUbPTYJ+vRLwP9cBvgqOi4G6wASAtqF3YvtDcJ50+Pq4Ewf+JppnGss+BP5p5LYA/+st00T+hFJn/e9X5pcRPD/6p2lcdfH/pXPLJP8P1M4AprrnQAHUSUEN1TuCgRINFHUGQ45WK4c3OP01z/LG01/L+mv3cPTsudJ+X6rooHyflIE3B/5whLlSKADdp4egAHRHE0FcIbibmtyeHH+dxGYCVcrA71pl3Zt9ccB326HCqAJ9oJLeyftVOHRL/yu4fbfP7xvf15y81WTx3/Gcf5XcSO6/rfUfglbdgi8wGZoZnmM/1v886Z/S/XrWv7mH5gqgrl8dDx8tAw0QvuAVPoA6Cqh8/GQoaPm8lNuxyqEE0pMKwh17+l0vsnnxBG88/Tirxy/TX9k274jNDyieY5kOMmezIO0oIX+fB+CJPdYBuHhg7dNDBZBre2zRp/RIAiUT4+/b/rKq1G4YqRKz+E2/clsMxP3r1IF91UuPLwAAEs5JREFU6X8QvRP2qbP0w/O0Bf22NE/sOm2Bf5oZQLs0zFtA1ARATesoLfdPJqzceqkrMZfUDCWZQQGFP4w256tqD+mSvH+k3T9HdH8p+qA8vZ3s69Ny7qWf7Df5cmfFjyQS9VAlVT+CZMYfl5o4z+SPVWH+EjF/buw+VSACD77/T0g6Y175/JOQST71d8f7vLH/l9eYQdOx5+3YRUOKuvI6b3fjKMZT9EuC40xb+S+/nsrswuSmf/inguvU/SlvHP6ff53iWuZPCaUxxcaePyMKWif67MI/CkdudL/rE36XFeepAvby92rOlT+T6wz8beP8bxvwj0moACYURAjwUyiMJuVS9+Dq9pVBsfpLKk0RpwX2inlJ5XmIg3p0f4UCiF27bkFpv18bjrNKISSSNf4YrqcCaNqv0Cws7PHAk19gd+MQbz77aLHPAcwUSiDsFwPEEBhjisABark9DsBVymGav5jCCa8Rjs1XFKHS8e8rVIhtQb+jsmifmDM3Bvr1wN40G5gv8M8itxXts9/In1D2k/U7ca6WkT+htA39nNeqX234/+Ke4vTPLPH/dWsAR59LhO9vEwUUjr3OCTxRDwhmooGcwzf0BWTe9Y7ddYFrD7zMWy89xNrJixw6edEbbdU1ypJf0aOVYvudfyCnktx+z09gjteldvAoH09xF4vgxMc1i9TRPuH+mB8gpHVi++qcuLF+bSiecnt9+OaNAv53POd/I2Q/kT/7Df2s6tN2Xzw2vwDiqnM0KYBYjR5zjmIFMHON5hBQgLoqoP59VEUBRTn/iALwr+WAPpYPUCiHeDRQzOGrxPVJbR/D8T/w7i+zeekYr/zJ+3j3t/47uv1h6ZquVITzCbjz+ArK5+BjvgF3H2EfoOQn8KW05SuH/DuaPGZWCUE/NoYygMaVRKyPP5O+noAPzbx+vM98QD/WVgL+ll/VbQ/+1zPsM3o9Ziv5PNn3+oR+lvvELetpo3+u1wwgDAGN339zIbjSvVUBfuAwbpoFtFUARsoO36qZAAk88sHP8qVPfjMvfeq9nPncp2Ajo/OnunQ/2kUn5WsBjbOB0tUD5ZN/DkI9Qyu/6h3z20IKr+0vpgmHQnCvmxFMC/ilfi1BP953OuCvy9SdFvhjUk1r3mGWv0LIStTMfKmfyetNR/3MGvc/i9TSR9cx+qdNn7YZwP7xTSGgUJ4B1D2T0r1VKID4c2tWAEAlDTQ5CzB3aPrYTY8qWj18ldOjL/FG9iT98w9w+AvPM/5syujXRyz99BLSKdM0sygB8Kgh75gJGsjrEoaSuv5uHPOWGLjVUT+lzxHA9/vUA/kkuLa19mF64I/dzzwt/pi0/bZuefCPyfVO+pon918X+lm+p+rQT/9H2ybzt25fGwXgn8MfR/x+6+P/m0pA14WAxsYdhnzGKKCJBWG8/mFoaNUMwJf4vjgoNymBbEOz9L89zdJ/fIqLf+pJFl9/i/7la6RfTcl+b0j3O3olBeSuH1JC5pkUtJDrl//32twz0945oaCJ/PsMxfcHzFOqLNuJmUAD0Fd9VqXf+6Tl3QT4/nF1yyfW95mN5jHna0/1lGsAtf+ubgvwD63/my37qfjZlvtvP5bZ6Z8qmdb6r6J/wIFzfQmIaWcA42145f/p89bvdukfz7jvh0Yc+UA66Reos/gb/ABNdYF8emacdhgNuwxHPcajHqNRl+Gwx2jUYzTsMR51GY26jEc9hhc67H1fh/HSErrT4eK3fIB7ful3YQ+GnxzT/47uBKBPAmXxbB0Q+MdUSfiOqrB75FWsooT2I5XAH/zGW88EIrOCGOD7n+NKYj6Wfl2mbhXw+1LH59c5dwvgb4eVtwX4z0P2y/3Pa7nHyb7Tc/9t6Z/SdfZB/0yVIFYxW2irAGIA60u2k/GpHzjM7gVFNjAW7tuf7PLIf7fH2R8atfIBQFEeItVmkZLdwQKjUY/BsJ8D+WC4YIG8z2jUZTTsMbSAPhq5vy5Z4wLlmk53RKc7ItFDYEjv0lUW37jI0msXTBcBtepWIbP32lIJmEt430NLrA7hI88wDiQfw5RZ1hPnqaMqIgqhzvFbRQPdKNCP9fH3TwP8TRZ/eJ91Fv80vP9tC/7TUj/Rc8xpofdY/7qSz/MO/awr/AZx2mbeCqAqcqitA9g/b1UZaICv/uJSAfyAFsVIenzl51fpffOIseozHPbZHfYZjvrsDRcYDg2oD4d9C+rmv7POdcXsIB9jMqbbHdHtDs1fb8jS8jbd7pCkN8r3JV3zOXFA3x3T7Q4hSfMSB+lIOP+fjMjWg4v0YOl7E/zooTyT2D2HibwVf39afLb7/QXnY/RQiQKKhHiW2pmOUmiS1rRPDQ1k9rcD+/D4OjBv268O9KGZ5im11Vj30RlADfDfcZx/G+pnv+We58n9h1KnTPYb+jnZb3r6Z5r4/zZ9ZnEAV43Vv+8Lv9sjG5gcxhd/9D9H97r5MS//f/Hx9boDer0hvd6AXnfIytIW3Z5pc8Dd6w3M596QTt42JOmMSJJiLCVe3Yr/TIv9Xpt9DqkWkq7mxE93uPhjY/TA7NdjOPRfJiy8WyiKOAfgbSOIgFa/bt9Z7NNDbY93cj1oH3feNu11YB/2b+Mgnhb0/b7xfs2g73+uA/62jt0w4TG8n7Zy24A/TCqA6x350yTz4v5DuRn0T6lPBVfe5CAO26scwFBfAwgmk8DcfS8cywCNIBz+3NOocYoaDOlkQx7/b65x+P49ut0Rvd6Afm9A0h0hUoBxGgFlv70A6jLYNzmD3T35voDcMRuEhi48Itzzqwm7XxCybei9V6HWDPDHQkh9JQBEaaF6Cd7K2Exn/vheK215f9O3HeBP7JsT6Pt9m3wKbYB/VsdueN2wbdqZ2S0N/nKj38gWciO4/4l9c6B/plYSUyqAaeL/y9eZbgbw0F/Y5e0/6JHuwfFP/Yk9uWblgYwnPrzhJTpZsI84gaFcEro0zsA34EiUaoevrlEQZcs7p/NEk3aEpQ/aXhpAl6z7eB5BoAi8d6vZP+BLxESpo76uw8+wiv+Pg1sDFVQB+P6+JtBv6tvkV6gD/ar9bRy75XuZj8Xv5JYG/1nkeod9NkkT94+3fxrrf7/0T1Xsf3gsxBd+N+OePgGsKQPY9G0/Azj14SGP/+gWT/8vK0hHo1Nh8e6UD/3cNiLF2OqSw/zxRZO/SkBdHw3kS2wWYPfYY6ucskFoKJQDNqJ9y/3r/APh+xJy/6YtnWibvIodQYOPpHRsS3Canw+g3nIPj4kBvt9/Wl6/ar/fXmft++1NoZz7VQb7An8R+SngzwJD4EXgL2mtr0b6vQJsYozksdb6g7Necxbq52bG/TfJrKGfN5P+adtvmgzgaWYAj/zwLme/b8DVr3RIDsPao2mJ2okmfnltUM4FiI25bIF7Ci5wQDflBfjHxDj4JpqnejZQ9K87xh0XG2ObtrhMb222OW+sT7StJeBDM+iHx0xr6U+eazprv6mtdC8NIF84fNth034t/98BfkJrPRaRvw/8BPA/VPT9Vq31pX1eLypNkT/zuUaNw5bZuf+Jc5VAsJr7nxzD/OifaaN/SuepcBBXz0jaJYGFfbsrmhNfZ5ZGrFNiVfcVnr8S7ImEiEaoHnOteJE4X0HElEAWKP/S/gqu3/U3YwprHAXPP/gptPcVBMdFooSmkZkVQJQCCRVAs5UfHtcE+n6fJmu+ab+5xnTAf70sfif7An+t9W97m58Gvn8/54tJIopUl2/seiR9zTvu31cArhrivEM/50H/QDlaJXb8fuL/qxzATQrAp5piCsAH09gsJqR7TN+KDOGA8vH3xxSDffrFw6oE+XZKoJkOcjIZAjp5TPVxxVb8vYmFk4b7Y1J1rmmk2gdQzX07CTOQqyz88NjqWUG9pe+37xf0/fa2oZx+m98+7YLu7cm7ZvnLwL+p2KeB3xaRz4nIx+tOIiIfF5HPishnL142cJqEqy/NIE21/m+01N1RfR382fa1SQGvsx7KL2v8XJV9Gl5a0x7/UcbPEf9x+gvCNF0vOobYVLvCCZdUAERTtIe/3+eblQcQBRjoMkD5/fzj0dHjkuD8seP9v/BcVX+TzzB+rlKfFuesHFNk/BP3WHGu2LOLHVf3fMP3rQ74S8fJ5FoTrj28dgz4E3Rr4J9FGi1/Efm3wF2RXT+ptf5V2+cngTHwCxWn+YjW+ryInAR+R0Se1Vr/fqyj1voTwCcAPvjehdbmwyzUz7y5/7rInyaZR+jnPKSJJonJfmYA5fO0SwIL+8aeQdV9TOsIrqKBJu41QgXFZgFV/oI2PoFiQfk4LRTj+n3lER5fHFfcQ0wmnu0+Zt3tqJ+YEp6eDmrP/8ctdojz9tNY+/612hkSDQbKHCx+J43gr7X+trr9IvLDwHcDf1rrONpqrc/b/2+LyK8AHwKi4N9W5pH0Ndt12/P5dZE/TRLy3/PM/J3s1y75q031z7BfU/u0IaBNpaCrqoE2JZ3FFIC5drwsRJUCgGqHb/i5qphds2O4zPOH4F1k+lYrgth5QmlSCvuV+plmxey0hsOPnbOeEmoG/XBfEw3UFK4ZtldZ/LExNs9ip/ue9hvt850YB+83a613KvosA0prvWk/fwfwt6e9Vhvu/2YkfU3D/Zv+s3H/E9ctgVl77h8mo2LM5+boHzP+6R3AwISiqAsBNe3xJLBwDDEru9xe5vubZgB53ybOv8TTF99i27BQJ/Gy0fne4mOQnFYV9WNk8rur4vnrXrfEhn/ut/hg/Nz1QNXWB9A0S5gmQ7gK8P3tWUC/kfOfwrFbbo+Pt+23td9on58B+hgqB+DTWuu/JiKngX+stf4u4BTwK3Z/B/jnWuvf3Od1Z5brvdjL9OOpVgB11v/EeaRd6Gco09b+N+OazgFcul5F+7xmAFWROP79QkzpVDij21A+DVRQ6FhvMxNw+6C+VEPdjCDvE7HgY7OD0jGl7/t6vv8NSqCFwxfqLfzYMdOCfl2/VnTOFMBfNSOq8pFVjbFJ9hvt866K9vPAd9nPLwHv3c91nMSs/+Zjpg/7vJncfyjXM/N3qnHU+iRuTARQ/XnqFUA468nH3jAzmLyPMtBDnArK22toHnPdyYJrbZWAG4+TaTj+GKhmgaFxo6WOtpjVD9AW9MN9bZVDVQ2eWYG/dI6K72AewA8gFTT9LSEichF49WaPIyLHgeuSs3AD5U64B7gz7uNOuAe4M+7jTriHR7XWq02dbunyDlrrEzd7DDERkc/uJ0v5VpA74R7gzriPO+Ee4M64jzvlHtr0m2ec/4EcyIEcyIHcJnIA/gdyIAdyIO9AOQD/2eQTN3sAc5A74R7gzriPO+Ee4M64j3fMPdzSDt8DOZADOZADuT5yYPkfyIEcyIG8A+UA/A/kQA7kQN6BcgD++xQR+XER0SJy/GaPZVoRkb8jIl8SkS+IyG/bzOzbTkTkp0TkWXsvvyIih2/2mKYVEfkBEXlKRDIRua1CDUXkO0XkORF5QUT+x5s9nllERP6JiLwtIl+52WOZVUTkXhH5PRF5xr5Lf72u/wH470NE5F7g24HXbvZYZpSf0lq/R2v9PuD/Bf7WzR7QjPI7wLu11u8BnscsKnS7yVeA72OfBQ9vtIhIAvws8GeAx4EfFJHHb+6oZpL/E/jOmz2IfcoY+Bta68eArwP+67rv4gD89yc/Dfz3TKyVdHuI1nrD21zm9r2P39Zaj+3mp4F7buZ4ZhGt9TNa6+du9jhmkA8BL2itX9JaD4FfBL73Jo9parEl5q/c7HHsR7TWb2qtP28/bwLPAGeq+t/SGb63sojI9wBvaK2/aIvW3ZYiIn8X+C+Aa8C33uThzEP+MvAvbvYg3kFyBnjd2z4HfPgmjeVArIjI/cCTwGeq+hyAf43ULWQD/E1MeepbWpoW49Fa/yTwkyLyE8CPAP/TDR1gS5nTokI3Vdrcw20oMcvntpxB3ikiIivALwE/GszuS3IA/jVStZCNiDwBPAA4q/8e4PMi8iGt9YUbOMRGaVqMx5N/DvxrblHwn8eiQjdbpvgubic5B9zrbd8DnL9JY3nHi4h0McD/C1rrX67rewD+M4jW+svASbctIq8AH9Ra31bVAEXkYa31V+3m9wDP3szxzCptFhU6kOsmfww8LCIPAG8AHwN+6OYO6Z0pYizRnwee0Vr/g6b+Bw7fd7b8PRH5ioh8CUNh1YaG3cLyM8AqZlGhL4jIz93sAU0rIvKfisg54OuBfy0iv3Wzx9RGrKP9R4DfwjgY/2+t9VM3d1TTi4j8X8AfAY+KyDkR+Ss3e0wzyEeAvwh81P4OviAi31XV+aC8w4EcyIEcyDtQDiz/AzmQAzmQd6AcgP+BHMiBHMg7UA7A/0AO5EAO5B0oB+B/IAdyIAfyDpQD8D+QAzmQA3kHygH4H8iBHMiBvAPlAPwP5EAO5EDegfL/A4oqC3JlCTrTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.optimize as opt\n",
    "import numpy as np\n",
    "\n",
    "points = []\n",
    "\n",
    "def f(p):\n",
    "    x, y = p\n",
    "    z = (1-x)**2 + 100 * (y - x**2)**2\n",
    "    points.append((x, y, z))\n",
    "    return z\n",
    "\n",
    "def fprime(p):\n",
    "    x, y = p\n",
    "    dx = -2 + 2 * x - 400 * x * (y -x ** 2)\n",
    "    dy = 200 * y - 200*x**2\n",
    "    return np.array([dx, dy])\n",
    "\n",
    "init_point = (-2, -2)\n",
    "\n",
    "method = \"fmin_bfgs\"\n",
    "\n",
    "fmin_func = opt.__dict__[method]\n",
    "if method in [\"fmin\", \"fmin_powell\"]:\n",
    "    result = fmin_func(f, init_point)\n",
    "elif method in [\"fmin_cg\", \"fmin_bfgs\", \"fmin_l_bfgs_b\", \"fmin_tnc\"]:\n",
    "    result = fmin_func(f, init_point, fprime)\n",
    "elif method in [\"fmin_cobyla\"]:\n",
    "    result = fmin_func(f, init_point, [])\n",
    "else:\n",
    "    print(\"fmin function not found\")\n",
    "    sys.exit(0)\n",
    "\n",
    "import pylab as pl\n",
    "p = np.array(points)\n",
    "xmin, xmax = np.min(p[:, 0]) - 1, np.max(p[:, 0]) + 1\n",
    "ymin, ymax = np.min(p[:, 1]) - 1, np.max(p[:, 1]) + 1\n",
    "Y, X = np.ogrid[ymin:ymax:500j, xmin: xmax: 500j]\n",
    "Z = np.log10(f((X, Y)))\n",
    "zmin, zmax = np.min(Z), np.max(Z)\n",
    "pl.imshow(Z, extent=(xmin, xmax, ymin, ymax), origin=\"bottom\", aspect=\"auto\")\n",
    "pl.plot(p[:,0], p[:,1])\n",
    "pl.scatter(p[:, 0], p[:,1], c=range(len(p)))\n",
    "pl.xlim(xmin, xmax)\n",
    "pl.ylim(ymin, ymax)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 79\n",
      "         Function evaluations: 149\n"
     ]
    },
    {
     "data": {
      "image/png": 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HkxfolbWKmZ7V0oWNjKdXmpT9Bshl2r72jlPClUt6RQQ0u7hyCNdm6pXDdBzbhme+Bv4Ta+0/V0pdBH5VKfV3rLUfjNm5lIgzxUqFt/qPt51aLV39ujGVa8vQ86TQx6Ebq6KnHrhzFBhb8DAFd26s6AOSkyt4uFYJxQf4RKJmn8CdW+uKalmjQId3f/GYRt1irCUoZhquv+Gygy49miJ66MnvVvDQcyVLyXIPHXFsoOWll9QuwUq8e6kdjFO0hPF12ctQs4zxxEvttuWRh+35trBe3vxL62W6fuOlFyjABMhTekWtNHoJ1alymvId68A8kSKalhSxEl54eIeM7hzgyrsoW9nXWPr13GBurf0c+Nx/fqaU+h5wGxgF5l02pfDWGDqlSMOQyhS7skHzBKLzBELHVFNEyBRlILT5LZq7uZQmejhO5E5YHU8MKwKj0JyQxgK+3rPVHtyMdSAs6BZrFQoH5J6pwSgVg6f4wCraOA9dWdAN5RFoHhkQdQOhRbm4b6PE7AMpoKfrifvmlEv4HXLaJfw/OTiXqJU+UJftgm0a+NyG5z6GtikBOIyLG4zxxkuBzrFAnj+d5TeHtdhfKlei9NDKZeL6qF4JQL7SsNYJvaIMrA4sZsdnes4MembQVVPfv5TtGROFSD+3vfXg0Ysn6oJXXuLKx8TUtsqZK6XeA34H8H8Xtv0S8EsAb9/OT/bzeed91qdqOa/1jTsF4OGbjcwETY6BwVCRqlxS3XngzuvkhtDmzkOavwvSCI9dALFRTYDHGHwxLgXeqw6A3gREnQsdakArbWJ2qNtdqnH8Reyce0oZohnMj1a5BE88VFuUN8exXnr434LJtqF9+E+kdXnrcb/Cf78NZcvUc3gsiJfa9gVD+4C8Lm0T3vRUjzysa0leW7QLiXceNOWJRy7oFV1DPQezcF45VUOxKG0aOaKyEch19oqVSgVAS8t15X2WTLQykl7eGs+glDoA/ifgz1lrn+bbrbW/bK39Xdba33Xtmh6n4X4FVS2lYvF5265x5GPP/9CW/rxwhy5ZH3eeewlhXc6dB+15Ux6XKFUkO76UJ9pMJWAhekW5ykW+Qj+JJ1ZQvcRtJS9xgENP2hZ4dOjn0ktjKe2Tt+0CzaSPghpl6mvISr/50PcotR3zeyVqosITxhjVigT53Cvvy/qUMkQZtwnvaUVEkbbv1SvVqcJUuDrlSXlbf93opmS0pFS6uHJpQ1x5aCPfpU256W/FM1dKzXFA/ivW2v/5PH3JuiWb2FRVy7bqnI/JCC3Vawl/bKJl7uDOgU5lC7RrtjRer6BbtMH4iSfChBbG0yKV9lSMNq7gFhprncfuHGpR/9wDt7GqRbcoZd3jrLJxMotcf7729FGSIQriv2h76PgxJdvDz9RBu4TtfbQLUKRe5PY++iVYFw0jbazMbKqNuoF0nOdDdEpp35I3DuP48Xx7Ds5J+wKQywJaAcibBDYdJ5uwVjXqlbrCGlr0yvxIodawvCoyPSuLntcOzJNCWiapvxKVK+SeerkGS4krLyUJBbplTHKhtG2oWRTw14DvWWv/4pR9p5S3fdVVLfGYIzJCu/brUvOMT+cVHJsqewqhXfJYKDwOOcWcLJPr6p83fbh657ia5zaoWppsUakmiBchJBdg/rgMqVfX56GPlZzmevR83/wYY3njsZ5u175DXvM29x96kiitz/fv2ievsQLnA/IhjzzP8FwbnQQ8pZ48Va7QplfOXK1yM4d6QZLpqTTRK5ea8jAvgKKctl/iyoEWVw5lIM9tSv7JNmiW3wv8KeAPKaV+zb/+6Hk6PG/hralp+F3bhqiW3v4TeqUsWewbZ9efmEbM25NXlDyB3FtQ2UmXn5hOpmgid96aO9RboFbczOUiwGRJLr4S3QINd9qiYoRkMbazKci793Z6f9NP89jfRbtMoV42AfWxdbtlX0OvMSaPPxXEx1JQXbTKFCCPfdH+f1v7F4BcOgjyXAvOhTHaBeut48ltrVC+vG11BtWpB/I9nxwUNeUmSnSDgsVVRqRNr8jrkfQ6C1biys9TUKvLtqFm+QeUZ4KbZM8zCJocZ4SqZXxf3XXOY99qOBCa0C5ZEpE8Vl6AK24LVI9K650bW8UxAK00f2wD4m4PFww15Jmifoo5AKW66RYcTWOMRinj+rPp3KGSboF2QDSaIpEsyrbhuDLw2WV9gVG5PfTfF/DMqZnmGOX1so9gz+NpcfxkD+VzdIhSydv00Spy+1iPXB4jXx+WhwKe+VNglCJaX3vFc+SOJ1dUJw7QV5ecV55MAyfolSa21FwPSeAT2wm+5+XKcznjV742y7YkimNVLeeRKZYmuGj6bZQoiTSRtF5LKxO0UIclAPpY7tzVc7Epd46bzMKohupw+BnUKJ4r91JFa227qiKCbgE/Z0XgzZvqisp6jXrMGrWE2jAxQ3QA0NP/spEntlQwGYeeK13cb9tWuzTnSDc3PpQZmp+bY8D9edpY8A42RDGVQBw6vO2RQG5aIN32yGXb3CuXPLl7b/TkptaYtfPIWbkiWtWJYnaqmJ3CehfW+2mmp541xeeqykRePPLlKihazHPhyl2baVx5sFcKzKd452O96L4ZiKS9qEBocsyOoGgzJgE6yhZ158V+SQtyBQlfc9wAUs6CVFF+jkk/0jNXRKliPL0sMThpjU/3j6UCPNirkCzkwLsUEHUH3wzQw7fOPfB2+j9JGyC2g9RLd8upxz1Vbz4G3LdpQzTMpiDu1pWVKlNplT6PPHDkcn3ukef0itSTW2hqBtU+EzlMNuEnnKjOFNWJ88brXTAL6wppVQ29on26fowhZVLEbXPl0s5zjrw4N6HDunjjocJbQ32U1hUntNiC3rc4pi0FQsdw56GdW04f5cLnkkRKcuftk1U8VsYZVWyUKkruHNt46Baw3jsKQagkzV8+HkNygZYeqSF4ZWUOO734U448f1TP23RNJp3fVEs0xBQuOt++CQ9+nn6GuP2uduG36OLGSx750LhDP+3xt8eRt89jK4kEFny8RglAV16C6KeBWypmJ1CdeSDfcVmeVs4cFBQqIuhZkiIiPp+XKy/RLfl176TKX3GaJTfplZ7HO590zAGqZcyxpWedfp+UdmmOOZ47l0lEXdx5UqelUCIXnO8bTthK+y3Wt/HetvE0jNEKjHXsusUDuYqdWKOorfsmYPyb++zYljRDdKZNS7IIsPZ0zBQPnfht6KVdQHC94ueX1Ev4j/rol+S/odsD7vK6NgH0TfoZK01s3cwKlErebopHngB15pGvTdM+SBChUUjJDM+Qpl9bJ0F0UkTPl69VMzHzynPkJ94r34P1BesmaF74oOfMSxBDpqdqMj1DIa0A7jNlBuiVbnGCW26Dd1dBrSlqllcCzLtAeRPN+dRaLX3jGZspOiYQKtui2hfMqNotgjuX/bkM0X7uXAb3utL83TbXVpbJ1dDUbJGZoVphZdpqBPWQ+l8OiLpjetwXNx+N69d9DiCb12tJA5bRVADh7ozQLtoFaFEvkAZJZduugGdXhmiwbdIuU24A2wBx6A9yyvZ9VRFTz7/tkYd3qVxp2jYeepAgBlliI0XU6RRwK0+vnCpmx2B2YL1HWkgrTDQhMj1l3ZWcXoHcK0898nSyifFc+XntpYF528dy9iqoWnr3G+Gd9wVCY5suj3wgiUgrS22bk8QIMGwdI+POUxBqp/kHbx2ChNzxhU6N0kxgobV1ul1lfR2uxjOO9VvCRWhUnJYOf3FqwFiLDrJE2iVzjUrBN3zXkoeuBQhPAXTXpy4CuuwvLg9w6sESpVHPhbotjzy3MVr3dLkfxKE/yCn36auKmHvkcr8crCW1ErYHJyGsz/XkzVyenl4JPPnSAXl1BmfX8jrlaSGtRoZro1euoEVDlixXtkzlyvsCn0NSZnf8r4il08X1c9B93NJY3rwrvb97fOExqTS2/n3H6NaH+pvCnefL8gSV/GA+iUXQ28ZEIgBFkT+PsxFJj8nmgazGC5P8uZzUIufToZtDL3mAJR69VMSpxKXL9s2xypz6EC89VXc+xcYcozTG4ncp8OJDapVQLKtVizyAMvlxVXLsLiBP1tMEPKVXHs6tpIhW8MqDDPHUceVm4VP2F74i4sw0UkShKe8sb5t54tviyqVtwpUHe6k0y4v0zhMJYZQVtmWB2yqN2+bZyzpx6eGPqaYYPXaCNJFiAa4Sdw46yvmcpXRL4LYjTw2e1wZrPWeuAn/uvqFCx0mf433D4te5SSyUVRjl9pH8eXhC6JIsBi7dyWgabt01psihx21+HH3SRKnyKSlegkkpY/gvck49WPEJSVy0L0Ka2B8MLQRue+iUfJ/co5btu/jxZF0A8gGPvJbcOU31wwDkMl3fBTt9ur6fbEKdafQK5s8U8yNYXYD1fpMgxNx4r9w21Erlgdyn7leCOw/g/Ty48twRC5+nijNeCc58rJWokXwWn77tY/t8niYpkU2SiM7FnYsgIPQH6qz01Gm8b62N58BFIS5tmwCo42cA2wREBc0S6p+rynPztluyGMaolaNtVE4nRUB337VFPRUCoyXaRe7jPrf5dPfb93Pqch9pU7jy+kSjZhY9H8+nD9E1XXGYTUA832+s9DC8dz1RlTxyaBLS8qe2VLWim3T9MNnECqozB+R6CcsrZXolmZxZ2ZjpKQvRAW0g3zJXPgTcpcJ8ub0yYL7NIGj3MTZTtUxNIBobCB2a9DkfQ18BrqnceXMiNtw5NMFQ40E8Kl4UhMxQ7Yt1aQ3WWLCqXYgLmoBo0J97T11rMEZHhYw7biEgKr+PIimbG75zCHzG5ey36ePRQ7/xNxJeuuuvO0gKbVCX+8j9civ9R8cf7vPZ//gOy/sLlIKLP/WU23/iE6r9unOfIdsGiOfH7k3L34JH3lBwgisXHnncTyQGOT25bjTlSZanZXVBNfRKNUyvjNOUi5jNc+bKx9orA+ZTbUiieB5Vy5j0/ucRCO2rptjezyZSxzQw2vbO8QFOMD5RR6hbhJolBEMDiFfeQ5GZobXRPqhpsZULciZ0C9Z75/i5Q335FncAD+B+XL5f6JYs1laBNhHQ43KwzENvmaIF6OE3ngrqOf3ijpidewWPPf3v0jEuH8358K++j1268gsWePrBJVaP3+f9P/PDYh/ShuSxXc7QWE9c9jEmbb8Y6LS6BfIlIA/0iuTI40xBcRlHr4SgZ5hsovZzeS4Vi6eK+VM4u6JY71vWez7Lc25QM5PQK1rbhF6RmZ4znU6O3qJXxLpt68rj54HAZ7CXNKFz2V6Edx77LIBvH+iO5dRz77yUEVryoLvoorHcec7F9393W0zzD2oWqT0v0S2VdpNAD9ItwazzvJVHdes9eGNc2n/IEIWyhw6kaf8UnkDCYiZdjH3E7c1vUFKypGn+w566+4/Siy3n13PLz7uH/+gN51UCy50dqvWKqobTL/Y4/nSf3bdPW30M2VgAL41niFKR+5SAXPZTSjia4pHLmisWf34kBbQKAc8zmD8FZS31ngt8NlmeQYpoEq9cJsp1iQK0AGugvTwA5NLGyBFLdV162w+2eM7WNYCuufGSfYs/0vRHlGK2aFCnjLwrDh6j8Kg1aQLoYpS7+yQJgZgwYUU48SSnl/N9pZRkWSY3yQwlzxAN2aGeXw99Rw/dlSE1VrUyRIPXJWeIybP9kmVUQueUVRrt5BRog05XdcUS+KT9N2durvqQFtUcPc7I2d0dqDXr2YxPf/IneHLzBgBKW1YP5537dR2nS1pY8sT7Mmu7uPEutUr+SsZW+j8LQG7DWH2dlYReMTotoGVSIA/VEN0UcJblJUW9g8v0jDMHtekVBUnKfji3c7AOlgP7WK48bsu48rGBzyEs+srRLOcNWJZULcn2kYlC57WhQGhXEtFU3blOaKCQCZrOHSrVLLn2XHvKI8wRWhUKcQ3SLVaRBERVmiEaNOyOhvE0i1+PFhM9e3ol0C9B5ZKY8NDDd2pZh5feai9Os1J9mxatltEwwbromGC7755w/IMDHt+6ga00eu14clsr5rfOJj+VdsVrikqWjhtY3k9fklAXrRLa5NtLQL4OtVUyj1zWXDFGU9feGYgFtJSjV06dV77zSDF/ajl+S1HvW+o94ylECHYAACAASURBVNQrC8eT6zgNXD+9El5xIgolnCSxHRopYk63hLbJrGQC9Mdw5WMCn3GfUa2es53HO49txQ8xtlbLlO3Sxk4pN2b80pPuqiczHOkunyxxPAWvoVTRTS63gj6ZxxJnXAm6c0G3KO/lJNhgVRMQtURwjpNZCA9syEPPJ7do1UO3qVdZCsZBFzXQ9rhD2z5vPexbAkzpuZeA9sovPKK+UPH0jWsAzJdL1Nxw4aeesbi+arWf2n+fNj4uZ1547omHffL2Oa0S9+nw2Ps88sCJS4880HnBI49PdTIxaB3qrigWTyz1ngfyBU5PLjxyNZJeKXnluRQxrBtj+ZNwXH8OTzy3V84zH8ObP2/vvGtMm3rtYwKh8lijPPKJ3HmQJqZPBGk2JEAuXwzqltqv8+FVSnXPtdejJ9PMKSLVglUxIKq8ky5L5vZJFutsvPFdnBMtjhtV9NBL+5e89HGp/ukx3bp+RUsLcPcNZ//mBfjU7beYH3P1D93jyu9/sFG+RaeKpQT0HZx43k83TVX2yMM6ecwuIG/fmMmoFRWzO8N7k+Hp9OSzY8X8ENZ7iqWvUW4WDsiJRbSm0StdmvJguUPUDoKWadDS+ri9I0loDLC/NDCvFP4x+3z2IlQtfdvGyhTHBkKljRlvqHve3jfVnRsxtkCvBEWJBCSd3TSChQBoAEG33NwIrK/ZEgKakTbxZv2Cr9jipzJ1nhZC6uiCqrZVwyWkB4VRyXQhrUT5gPyHUIEiKQdGJfCPSSIaAvWwb7ASFZPb8eEBX3z2LlqvMWbGN/7M95gvhj3yrmO0t28PxJN14j0PdObceR+QWwR4eyCPU8EFD10GPAWY6xXopWL+DHYeW47eduoVs5AzB6WTM4fqn7L+ikJw4flTacfTK3Q/fW+LK58SBH3lPHN4saqW4vELHvR5vfO87zQLNM3gBMRNIfXUc4/ctS0pL4a587CsrYooGaSNUXsepIM6vUCrUEXROqWJDUexLuHIhj6DkkXMEarwHjoWAqATNOcmmdQiLKOJHnq8BKyKHHq88GwZ0F17eQsoWPjKI0Dd/ZftzNDw2+eWK2Kk/fCD76K04frNL3h0702qeT0I0F3W5Rx0BUWb/YYThPq88ZLHHkAbiNUPg/Qw58hDOdsQDDdSghjW18pleNYKtXTVEGdHmvkR7DyxnF5XrC5bV0TLT8xckiE2GZ6FyZkT/jvlvkECvnkuXHlcL7jyV1qaGGyMdz4mAWdI6jeGSsn3iX0PSBHPa2HspRT/tF2qOy8FQvt0511p/mFZShWBqD3Pf9foidOmW1wSkPeudZtuURQAXbnJLqRkEcoeeu1vIomHHsYXzgFFEdAjpdIRGC1RL32g7v6Lsrce+xQXYRfAHz69yBcfvcu73/oNDp9cZu/CUatdl/U91ZXGE6zLE2/FAEYCuWxTCnSW9pNAPsYjN2Hqt6yA1vwQdh5aTq8pVgdg5s4rjxMzJ8oVG5ODptIrQItH76uDFNt0cOVdNqagVue+G+31HGzqQM4rGUzvmgWOakLm1TYCoaWx9MkU5ec0waD8WNcXDA3LeTS9S6ooH0tDAKm5KAKH7otx6SwQ6i1MBF2SLJroxSshU3MXfPTkbBM0KwU/S9JFk4BLppPOPEpIg54pUI2TJg7JEo1V/OiDn6aarbnzze9zfHTA7v5R+TsVXsU+O45ZKprVF9zskhs2Lx098i7FSv67lTjy+N/6wGdeBdGEc6QA5NWpYveBpVrB6sDVXWmKaIVqiGnQMwD3WHolWB707JMijuHK+5KE0v3EMfueKnlFaZbcNp1ObriWy7gp5fJtYxKIcu4cSjx7d5JPXxJRHXnv7pot0uMPgVGZ1h+482Q5O4El3RKkijNtYiGuQbrFkaFO1ZjRLSCWFV4G4/XoCpTy0sQgUcwKcwUPHQL978eEWGkV1rZLlsYnkD75orQC/RLWSOuTJpYA/dnjy9z79B3e/c4H6MWK0+N93rj1WecwxlKMY6WJY+mUdF2bGw/vCYj38OPGNpmdeV3ypnCWf19rMApW7l2fugzP+RPF4gnUO3B8U7E+CDy5den6MydDrKp+ekWrtJBWiV5Jgdz2AnmwAN453dLHlXc5cl+Jqom5DTCaLdtmkaw+KmaTQGhrrCoNhEruvUS1lMY1li5q9s1pgsC5QwwrWuKyDI5GHjqblQi/PmSGDtEtKB84DTMTCboF2pSLrLIYvHxQsQBXrnIx+fckO4cKtEtsr9LgaH4jbMUfBpQsOQ0TLAfXcPH/+IPvMpsveecnfsDydBdrKnYvHE+OC/U5OlO05SXwlp+7gpzhc06rdAF5SbUiPfK4LnjkPuApMzx3Hlku3DU8/HYlAp4OyKms05MrmxTQKtErEqylVx5MLkeBAN0USw7esp8pnnj+eYy9MjRLbmPmBp2yb3rXlD9Y9+1jTJ3z85qsohZsSJrUn2zQDrxILXuflbTn56FbQtAJFV74V/r/OA+eyJFavIduG2la0By3EkoyoJAAEkzSLjkANTRBub72EP2Sb3PLmpzGkFZbxaMH13j4xS1uf/P7qPmao8MDABb7x8X2fa/cSsdufZ8OCikst3+rYSDPj9XlkUuOPI5L1CW3+SQTa5HheaqYHSsOvqg5fKty07/tEKshxpR9lc7nWanyfJ55Ia1guRRxDJBLG8OVdxXUKl//w3jz0j3z5yFRfB72vAOhwcYEQotlc3PaRdAr7f2rVo1zFElwVHqlbj+/7OmW4KmngUMH4C4ztCmVG2YmkrVblGp4c8BLVGxTZdG72NZ75sYoJ3v06hpHs0z30FtldMV2Nw75FJQpgvLPmZJF9isv5JI88aMPfor54pS3v+EKaZ0d7wOws380WVu+qa48396OH+jWfqUYwyYeeVSt2OambS3YMPF3LkFcKvTKlbTdeWh5dnvG8jIYrydvqiHaVpZnSA4KgC0plhxwc7oFUtAdw5XLPqdw5UNO6NDN4aWDeZ9NlSg+D1XLFCniVM35UDXFXJrYVYBL9jOFO2+OUxW1580JbQYLcTVp/hVog6mrSLdYq7CVccoE7VA80iuBboklAHA0D7i5N2rtPfl+Dl156qfSgre2yk9t529EuO/uvn+HZaA+hvgbAva87aO7b/L43k3e++n/zydJaU6OvGe+dzqJSgvWFxDtazeGTkm3DYM4NBMzh/9iiCOPafqyCqJRLOyaO28/RGG5/+EVLv36gpNrc47ecbMG1XvGBTz9ZBN65mWBUY6Y0ithGrgA6mFy5lnCm5cnneiTIgbrq1deUsK4tgWhQiJN/Apx5ueRKD4v3nxsws42Zicak0TUxZ2P0d7nHqUE58Qblze+GBwNHnpKv+R1zwP4h2SiSjelcl0ykXXusnVSRDccGwOVrlMVU/5RNnroCnwf3Ry6RrkbgO9L/iLScwcP6v58az1d2IYfD3x685t3eOiZR94nUayN4qPv/STz3RPefO/Hcd+Towssdk/QVfeFO/bJs3Q+dPHhcnmsJw70euPQ5AKUSjRIjjy+Fzzyb9/5lLeuHsYx3b75mC++fcDDf3iH9a5ulCtysgmVVkWU9IoE8iF6pVlOPfAuG8uVS+vyyjdV6r0SYC5tahC0y86rahnbd2vbFrzzsSqX/LhDunO53OyXpvnn9EsAdKl4gW66JYC4Us5bt0ajlIqgHtqHiaDdu22qK4bz2HvqAd+1DXRLU5gLZd0NQ1nQTnkTlsMTQy/tgi/FSxvQQxu37zhQl8dL1on/6/G9Gzx7eJ33f/ZfJMB9drzPzv7xZKqw70be54Xny1O8cdmuRKvItuE998hTIA+acmIVxD//C7/CL954igK+XBn+wv3fzbP6gLcuH/LwZx9y/PF1F/CsbCNDjOVtm8BnmJhZ0ipD9Ipcdp/TWFJf2v4QV96VJCSPU942DPBbAXOl1F8H/hhw11r702P22QS0X7R33tpW8MCfl3fuaBFa9IocJxBlimNqtsjl4J3n0sQA6AHg0xN2mG6xgJs4QlMb79H4ZXAevbbW/VaGFt0iJ7UI9VuUBiGSjJNYhOCWBUK1xUo3j/bB6+qlXfxNqbbNtHStC0f+9Mm5Me0MthY++d5Pstg/4vq7HyXAeXa8z8XrDyYrWaCHYhkE83EA7sbeDeLQ0Coy0Ak0IB6rH8rMTkezYBVmrRyQrxS/9kf+CpeqBQGe/ou//R/yd3/0M/zhP/7fcDy7zFtvPOXe/SvulAr0iufJoxRRBX7cxvk8FSRVEAO9AgGo0/k4S/QKpF56KW2/tNzFlfcV2Av9yD77bFsRvf8W+MNb6isZ1Kumatl2nfMhG4xydwVTCo+Lpbt7t8SqLblqn+jd6pZwIYWyogF4ncckqitKtQs0NItVjcoleG/QFFuy6Ut6gCG5qBZBNvlqVVn0yo5c8ZK/IFeBlBUwwfJ1j7+4yfHjK7z9re9H+aexinWtWZ7ssejwzLvG03e80vpmOU34ydt0USp5IlGrvgoNNy69calEKqlWjJhg4k99/W9xqVqglAt4/96/9p/zd3/0MwD86SsfAv48lxmeWcAzSgxFaVt5XobzNV4DKgNyCcrZutRLbwPuplx5bF/ApDFeOWzJM7fW/n2l1HtT99sWpZL0qbp556m2qce/KdUyhl4JhbDaZQem1a0Jnnaa5t8OhoblqXRLPhF0MmuLzqorahvT+R23gnfxlS/IZROVi+TQXZ8EVohQcqzRsXtAKtAu7hs2v4fk0uW20m+Xpvyn+vIS1VIbxae//h12Lhxy9fZnyRPA8ngfUOx4WeJobnykR+7WtfnwvO1Ybzxs67oBSH4898ibNP2MI18r5tUp/+l3fgtwE3J8/S//pTi2X/z2P+M71x7BoeX+8b77ozM9eQ7keWnbIrXSQa+Ecx26HZzQvuvzGK68ad/vtI2xF8aZK6V+CfglgNu324C1iURxCoB1qVrGyv/GqFq2JV+UVEsfuI+dvKKPO5dSRRkMzcci3wPIx+2U6RYH7mBw3nkNIiCqQPswo1GxRounxluAjvvYcOiB1o+g7d4DoVOHoKvRyXvr+9Hm0qHh05UqcOnyt5HnTkGCGPZ59OktTp9d4r2f/+fu5kQDgKdHTpY43zvZyBHpBvUs4/McIB7e86cXiwTwFMhzjzy8E7YZYrBzd+eMd24/iGe7BHKAv/RHfgVj4ayu+PLuVdTMQuDFpQwxAjetp8W+QlqQg3EZyLvS9oe8520W1OqyFwbm1tpfBn4Z4Gd/dj5p1Kkkb5g3f1HeeamS4qalcXPvPA2utaWJwc7LnRvbSBVL2vP2sj+umAQautUtQbIIzhNv+HPjL2yLdfS588Ip6c9VyqErMBWoWmGtQXsEkB56mEOUMCOR9n16jjT5Ojbl0t23Din/XuXjgb3X8tPE//bWKD7//rfYvfiMy7c+b52bp8cXAJjvbwrmHTrzHlli6fNUEAcEN55x5Fa1QDxQLCEhyBoFS818vuLmrSdoBX//4R5/+lf+QjLuH/25/xhrLUtb86u/9Q4rW6Hnru6KLqTrR+WKB/KZXx+85TQQmi0XuPH2cspjb5Mrl/0kx2Z4kppXSs0ivfMXpWpJ246btKIvELpt6yuPO+b4Jd05kCwH2WFJe56XzZVtIufBMN1ivSfe6M+1p1ssRE9d6M+Ddw4NoGNR1qlgHKo70Db+RFHK3TScesZ7xd4jz2kXOcZgpXMu0i/01EzP+spVLI8+vc3y6IB3f+evYtFNsBeo7805/uEVwDCrzgo9+993xLm1qSSxD8TD9gTYaQC+5I2HdTIZKMoPY3an48gxcPXmU/8wpltA/sM/++dcrgKWX/zf/01W1U4z0YRqQDzoyYN6JXjheWnbYF3LpaBnUlhLxJCeB1deShL6SunMvyrWV+f8hY1h4OaUe+RxfYFuiTfOwIN7rryrTG5b6TGebpGTWTiQd1uD/lx5fsX69e5rKUG34Hn1IGsEtNSaOw/N+rtAkDC636RNu7S05xmX3soUzegXyPj2Do/aGsXd3/wGu5efcHDzXgRMa2H5v11l9cE+p+9cZLa34ul/dYcLf/Iu1a1lsS9pm0oS5ecxIB6W4zr6gbxVwtYDuTFOtSI5cqUMO2+cMfcSzU/+yc8n4/6VP/GXqTGcmpp/9+/9AT7nJ2MlRK0aPblSJEAeg5w0VEuwnF7pEgaUbEza/ja48rHgndu2pIn/HfAHgTeUUp8A/5m19q91thef+zzwrm2SapHeYqcGe4AX36SS4hh+fFtUS18BriRDNM8ELWWICnolnDRhRqL4ewRv3bnBg3SLVpa1kB46ktLTK8ZLCmMSkYnVFd3Fbn2WaKBjdOTIrQFfmasB9FBVkUDH4E8UjbFucummwJIYcka7yKxRKWGMNyz/nksWZSJVCJb2UTCPPn6H1ck+t376V7FCgrn+3h6r7+3DWrOe7zA7W8GZ5vhv3GD/P/osBndL1kfF9AF5Uj+lR46YBzdhHIgDLemhqR0EBhAPk0uwhvn1FUpbLJrDL65z+uhaPN53/sD/yX9d3+HwBz/B9z69yZnZRc1dJUStTUqvqCbgGai91sTMI+mVvkxPaLjyMfQKFDz0Yobn8M1kTC2obalZ/oNt9NNnk6d8G8GbT834hH46pU9zvg1lSy/1I2mYjDsfmyGqxQ0g76+PbimpW8Ihc/25tVUxIOqmjMMFQrUDPRU8bXmuB7okpP8r8HeeYmA0BFtz2kVmjUqnoRjo9O+ty6ngrct2ptbc/8HX2bv6iL3rD5J+1792wZV1BdaLOfuPT9z3WirWny2o3h6eNm6smmUKiIdlyYvnnHmuVgn7dgY6LdhaR48cA/rCKv5+j3/8Dic/+noc1+3f9w8426n55PAqH39+mXq1QM1tnDEomcszAjKdWZ5dapWwHNer7jrlbl3Jsy5nfrp9O2TDE7nysfZK0CzyYtpW4a0um3JTGAv2YzJCN7WSd57fGLqON1SzBXLuvLkBRBmk32cM3RIuLAMxgNk1d6hVlgoH9o47d1miWJ8hqh1gK+3S+oGMQ4dQxKWhZlQs0BUCpS442qZd3KjdWMIMRm5d+7eJ/0XcLzP5pCKA/cnH71Cf7XL9Z/9l4pVrZV1FQMBojZnNmC8b8LZ1u0Ban5XaDgG4/CyBOrzbbHv4XJvGAweKapUoPYSoWJGTSzAzKK+BqNcVKwHkt37/P0Qv1pysZ3z5yWWMmkU9eT4ps5Qh9ilXlMqBPAXMnD4pZ342+wzlpEzhyvu2NZPbhHF8hQKgQzam8NYYVctQ8a1tBEKfV5XFXNkidecl73yKVNGd3I32HILTO45uif25PdEo1v4UjDclHeb6dLSItsrPGdrQLiFDNKpXoAzoIRgaxhHaK4XydEuJdgk3Fi1oFjw4BeolfB7jqcubW6BhzLri4Y/eZ+/aQ/auPU7AtbYK/d0T6s/nrGc7AMyWy/gd7FurUWBuO9qMqVHeBeByXU6pQAPigRtveHGRCBRAPdAqBlhrVK3AWOweji472WH9r34qjmnvX/9nHNYV62dzTp7sYFWFmjeeeMjwlPXJdWGyCfmSgVBoaJKp9Irbt829y+Wu0tR9XHmpoNZYDj+3VxLMtzU3aNJ+i4HK8wZCzyNT7ByT5P1LAdAsMFqSKsobWIluScc/kExkg5KlPyAqC3I5QLcY05TUVcor/CzEgKjrEH8g55GHtuCySSvfJgRWbQAwFzCz/jev8DcR8dQQKRfG0S+IdsEef3iHerng2jd/2KK5NBb13RPUB3usDi8BMKuXMDNUf/yxo4xGXs9DCha5bAvAPgTibn2mVKFMq4T5OhPpoVesYCzsrmHmmbFHlzEfvx/HM//pD1hbxXo5Z3U0w1rtPHIdvHIjJpposorzgGeJXpEeeIlegbYMUZrUlE+VIso+XPtpXPkUe2lgXuFmWh+y55El2mWbFN/aJBC6+fjaMsXWeDq487RNuUBUXw106Y3ndEvjmWZ0i1VRIZPrz60A61CQC5oM0dqGuKYH5OCJtzh05TbIwGjg0hXO447HstGTBEe71L6ZpF5c8JNIF0WlTgf9Aimwr1cznvz4a+y9cZ/F5WdJ+xBEpQL17z2i/ueX4T7Mf+4R+meewUUzGOPIrS/oCWUvHCiCeFiWvHjYJoOiOa2SBDqtlx4aPJgb1AV3FSsF9v4b8MXbcXyz3/H/QGUxa8X6ZObKHs9DJUQpQWx4cgnkMl2/NDGz+3+66ZVSglCXpjxYTrdMrYzYZTlXPpZigVfUMx9rUwtvnR9Mp9U532YgtI87L461hzsvjbvsedoI3mnfaaVF+e4okoZ2qD2gS0DM9edhujn8RSsDok3JW4CA8B7Aw7gCoEOjU/fBVERgNDRXKvTtjhMvsYQ7d166++wOG1QrfaAO8PTDO5j1nCvf+K3BJ6r1/gJVrdG/+2m8GeU21EdfwFNunwLiYX3JGw+0SpAdJoFOk3rkaq2wu4G2AvvxHXhy1R3g0mN452PWZ3N3g13ifoCKpgKissWAZ9CS5+n6Ob0CTXCz+dyvVglW0pSX6JW8fevzCK58UzmitJcK5tI7HytR3MaEFXk/U9L7z5sRui0rShMLgdEh7hxoMkHDOl9VUUoVJVce6BcAnXn4eTIRXkUST25t3D6+yiHgJ7XwXLo2PvnHceY1BckilAHdilWed3GcuffwlfVo77x/Fbdb4Zo3sYSGOydKGUO2qFvfXOy1VSigXs549tE77L15j+rguCnR601WdARYHe8x2zuNAdIpgc8SZ97JkWfrcgB3nxvAjtvoB3FJq2AVdq3cf7NWjiO3HpiVC+xGIL/5Obxxj1hQbe1/6GySiSBBDFx5zOxUqQQx4czJwH0ivSInnegCbkmvbJsr7/LKh2qqf6U981fFtp0RuknwtJTyP4Y7H+ozvQGkhbj66JYA6JFWCen+wruVHnqlrUvssarbQ5eSRUgBPZ7nHbQLXvKIW2E8dx5KAQRPPdAxgU8P1qJfaAdCtbIcfnQHW1ccvP9hLzCHfdcne8z2TzqDmX1W6r8E4HJ9F4iHbSVPHHJahUatImkVC/iApzKOSgoDsesKPrvtlt/6DPXGfdfPGidXrPB1ycseeVJ901NzJY9c0itagDJMo1ekSeDuCk6O4cqb/rbLlQd7pcD8vBLFqd552mZzVUu6z/kDobGvCUlEfd+n9Lt0TS8Xvrfkzkvg7froplvkzEQRtLO2kAZEK+0DoKG9kCwaHxFUIRhqFVbbBtBDcNSCzDJK6qV7PTrK+qeBRsKoVHrMnE+PRbd6QH11Nufok7fZvXmX2YXjljecm7WwPtll59qjSR55sBa90rE958z7QFy2M6Zp30gOhYrFOG/bWhJaBXA/SnhoenqAuvcOrObOI7/ugByL09prvPzQxCqIXUDeF/AEEiCHJng5lV7po0b60vbl+qZ9+xhDNoUrD/ZKgflYm1p4q3Pf83LoBTplTPsSxbMJd+483TK9kh9zTJp/zgU3Qc0N6RaIvDN+zxkGoxRro4sBUS0yR6VkEVxhLo2Oy5jG03bIJAA9uuX9tIuqVQQPN8m0X/YAD2A9jx6ySJ3nTszStP7D0YdfA6PZf/fjmEyTZ4bKWEK9nGNNhd49jTRNn3X5NkMBz3RdGtQM7XI6pfU5qSFPplZx76rOvsHpLjy9jjq6iJ0vUV//Aeyd+EGDPXWBTjToeY3SxKSgkgQxZHgOBTx1AtLdQC7/D4CSFDEPeibbSp648NCncOU5xZLbEMUCrwCY96lankfhrfbxp08pNzYQOiYj9LxWpFcGwL0rzb+vTO4mdItUswTrCog21RXdDEVxf90AuvTQrVJpHXQlkdtb8NKDB5rRLsTiXioGSJVKPXWlRMKRv9EGUJfeujlbcPrZW+y8dRe1u2yAVDyFhO8v+XIAvXuWPK3kNuS1lySHcr30wNP1bRCHhheP64LXbt1EElgatcra3djVUjXeuAKeXYEHb7nI8+WHqCt3AQOnldsf99vja60oTa9HHjI8w7qugGfJKweK3nMXvVLiyiXYlv6nvungQp9uf0m3TOPKh4KkLwfM+wpPbGAvWtWyiT2vQGjrOBO48xb1ktErm9AtgfFoTGrWLcaDYKRZxNNADDpqt5+yKkoWtU82sg5lUGgfPPOVFMP/H7zwFufgPPE8yShu1p6v98eJSpfMU09A3X0BtLKcfHQHgN07Hzvw9FSM/wWy395ZfbLrlnfPkPVNplgJvN16WusllWLF+kCnhISgwItHlQqSG3egntAqgY8KHT9+A57e8AOp4Ml1WJzChafoQzAL4IKBqCHP65KLjM5Ir5gWkPen67d57qn0SklTntsmXPkUumWKvXTPfNu2Ld58G6oW2CwQep4CXH3faQx37vYZplskeJdquUTwtm6bpiliZSDWbwn683C8XLJY+fbWe94uMCqSijRN2n/CmVMAdU/H5ElGYrMsmRu4fJd0pOINRYI6ON57+eUNFm/dhcW6AUnxSKDFzx688/WJ88zVztlGnHlbgthen3vhyTrBifdRKlhSyWEA8zWRWrHKOuD+4j2oF+3Bzk9hBfpUYfbrJiEopOgLWkUpEsCWJW1LQJ6n64fPpffUA2/WDdErOZA/L678PPZKgPk2JYrPwzZJ7x8zvi7NOUwD9E2587RgVvsG0Ue3hBM0n2Yu3BhaF1NWXTEAug6gKCcEhtakFjaWAXDSxRrdTvv3DwYYfGCUBq0DsKtmvetOxR2twj/up3w6KvDp2nvoDuCDx7786B0AZrc/izSM/O7QPIEEU8rdBNR8iVG2Ge8Ey8G8FejM1jfvJX6cxhMP643jw2OAU3rkZ+63iLTK6S7ce789yJ0juPER1DA7VDADu2fR8xoUVJWJ6iUdPHPpiXcEPGfatHlyNaxcCety7jy06aJXZJ/FySa2xJVvSrHAKwLmffYiVC1DtVqGx7hZIDQdWxvQp9gm3HkL3MXvs6m6pR0gbbxzhdlJggAAIABJREFUme5PbOmfArxHnnjvECe1wOiWh+4AyM8cmqtc8MtGuN82cDB+vcLdUWyhHAAqfI0ol0w5dddNfbzL+v51Zre+gFkdaYkgbwQSOiaYtQpzuhsplinWlRQUvrJslwN4s34AxAWYI8BcrRSzpxozt1jvgNvlLtx7rz3QW78Jeo2uFZwAGlY3VqhZypEHj1wmBQUgDxJECeR9Ac6wrvS+bXql9LnVbgtc+Vh7JcF8bLBzW6qWUf0PBELHWOK5F5Qt27Sx3HmwrmBo2ucw3dIcO63d4qysP4+gjwh8BhpFWUKVRQ3RQ7e+5orylRZ7OXTIAN2vkJQMeYDUt1EqxlADqM+/VFz5J5rFA8WX33gHDgzVW19GgJSqmHDoFrgD9ekO1cXDVmJRl5UckRy80/dmfdsrJ+HEsV5qaL03blTzhOPBXBnlvGsFdua+iDUK7r6XDur6J7D7DFW7wKiZGbhmqBd4IE858qYQmgdlXzwr98hzmgW5XvDk6brN6RVp0isfmxQU7Lx0SwP+r2IAFKiUoh5ZTei8qpapwL2J9RXfmuq5N31O487H1GwJahagJVXsKpMLDNItjRvbeOxurfe84zq378xnhhpl/cnux+EzRNcB4LIqi8FDp2rWW8+tWKPRFXGZCFQ0dEqkX4JrjadZPEgFgFe4BeGRWwW7dxVv/i2FXivO9nY5ObjC5c+/hH3LyU8FOWJKxfgfO4v7W+zZDuqNh8iaJ27/1IOP4zSEievTbaTAnb5n4C6DmoEzl564oFIwzhPXJ1CdeRpMA9onCX3xTRLbfQbXPnVX0UphK4s5qGFhUTMP3KHWSuVnCKpMSpWIKoj+n4i0Swmk+4DcbT8fvTJUf0UCew7kL4orD/bKeOZjC2/19tHhnXcfs6M0wJYCoenYRtRyGUG1jKmo2Obi+2u4SNmhG4dNwLvpt5tuSftsPPg8GNp8z3JBLmCchx7GGj31ho7By95iQDTQK96zJj9H4naIg1Be+eK9f+s+cuWfgPaJMY9u30Sva658fh/uVxx929EHNjj0qgHSEFQNn83pjutw0aZZ5LJawoX/a4fFRzOwUF8yHP6eM9Y3TKttH4CD4NK7QDx44n59dajRZ1614yO4FkX95OtgZX4s8NYPUNXa/YZLMBedWoW5DHR6qsRr+oNqJVGrDHjkpQJa0KZU5OdN6RXZTw7kQx56u4/NuPIp9nJrs0zwzqfaeVQt5z/2ZoHQdF05iai7j9Q7L9Zp6Q3eDksVY9sC3ZJz5eF40mMPFsBbUjBS4QIUJYsO1N32QHmojEMPOnRK1RYDbRKjn8LCcpCEhHY4AMOD8+KhW1dXFcdXL1GtVjx74xoHDx+iTgx2z3vztvHEQ7XG0K3jy52ShcUyqkpKdvnv7TK/r116PDB7UnHp7+zx8I+dYg78+FpeefN9EhpF/hY5iFsFa4U+U8yOlPOstIo/uLWK9eG7Xlco7K3vo7wXjQF1CvVlAzOLkx6apowtCB15W7VSSgoqKVfanHg76Fn2wKfRKyVw75IiNvukYyql7ncBebm/cRQLvEKeObw4VUsa3Bv2zpvx9ataxtIpJc15X7ByG5ZMZhEsSx7qC4Y2+/QnE+V0S9w/A3TJn4s1DaCLTNA8qSjSKt4bDyoX+R5qa7sx22a/gNEG4bUjyGexHNZ5j91qy/oCVI+hqmve/MFHPLl5nYdfu8XDd27C549RbzyEg8NAtbsew+8n6ZNTNymFna+o63K2aPVYMXvggHw9n2OVYr5comrY/d6MZz+/9p1l1IpfF0E+3CyEfjxSTwHIa9i5p6lWrm09d3+PtXgQ30nHdumHqKrGLj0N5U+r9dXa1ViZuZuaDu86pVWqyp01uUcup31L6BUB5GN48nbdlfPTK31SRK1MJ5CPrYzYpWAZS9e8UmC+bevyzrtsnBe9eSC0yKtP0KFvgztv91nWngdA34RuScG7rD931g3ooV2Xh15pUg5dSw9V1kOHJDAKDZi51pEvTwAciAMTvPqjn4E3/5FF13Dw6AkHj55wemGHB9++xtmzq9gn12DnBHv9IeraQ1QV1eZRsgh4msViZ6vI4+cPC9WjHZ5dvc7JhUusdveYn53y1o9/C2UVsyc6JlQ1X6Xxvt3voOINywbwlu9+u6oV84fKA7mKckNT72FOr7eAXC/uoVQN4TetYH3ZQGWjR06gVoJnHamVUjp+v0cOTALy+PsJD35TekXu4/qcJkXcpg0V6HqlwTzxwFW3RPE8qpYxNmXfsbMQjZIwZlTLVJvKnefaczmOKXRLaSLoEFjNPf5QkEvy6nKGoq6kItdjm0MP1Ib24K6N16CLRjbqHiGpvKhIwTx2SgS+o9tw/3darv8LUCvXz/H7Z5z+1Oco9QU8uQKPr8Fnt7Gf38JeeQTXH8DeSSJptGc7sFgSSt+CA3u7mmEfX8E+vsL66ICT62Eslit3v3S/g7acXZcTbSCoJFIAj4BOEcTVEuaPFVXtBmdtxenyG662eIcptUbXUB3B6qp1tEoVaBX3rivnkatAp2T1x6VH7vpsq1XSQOYwtRJs09orsZ0A976gZ591eeVDXPl57JUG85dhz2PC56T/PnlgD9WyqbKljzvPxzI0iUXkt1ugXqZbjFXJjSinW0r68/Dekiz6YznGo/HIAzhWMMpDb3hwsWyV48pzQJfv8Ssrnr1f8ex9g16BmeM8Da935/JjuPIITnZRj6/B4yvw6DpKn6AvPqB++xFqZuBsAfOlnyezgieX3Y3g8MAdbPcEbn7O7LNLrKsLXPvic3aPj7FY7AyOvm5cnZRknAUAzz8bUCuFqmH2TDM78dtmitrsslx/jZKp6gS9cw+lT9E1zI7dMNch0BmneDM+viClh6TSw4JHLgOeeeXDUsBTniuJsiXzwN36fnpF9tenKZ/ClW9qU5KEcnspYC6h4HlIFMd451N58424+ZGB0OeRRNRlLW+9pGZBTGgRQDmJF1jyiS3Cfn10C+QZo8EauWS8YahGsqiVjVUWXR9tDr02/kKIk15or0X372EyBbS7GSgcADeZQsSAqRxc8JojFRJWaEy4emq/T+hXKZgv4frnXP/hXer1ZY6uXGNl3kE9uoW98hhOLgAG+6OvNwC+OIMbd90MPLtncPdN1tUFFupLdpaPMTM4edPy+LuGutKuDngYYwDr5qduPHDvkaslXPhUU526zPt6z43VAHV9hZV5s/O8mc0+pjoDHe6OwOmbNXbPOA881CGPGvIs0Km7OXIg1lwJwD0LHq1OPVrpkZd48uiRZ9x5sy6lV2RfsZ3wykv0SrI8gSsfq2BJSwl0B1Jze+U8821IFKWN5c0nUSlbDoRuPI6J3nmfSQAveeRN6YDN6BapPy8GVmk89LzqYslDL3PozVhTnbdP5PFBtPhTJBQFZdolbFeuBnrkvf263GsXBDmXP1Ds3Tdo85iLDx9ztr/PvTtfg6eBO9FweBF75YHz5ndOm74eXkPdewt76RFnt+7x2bfleJW7SGwbzOdPFLv3NGoF9S6cvmEwC0V1Chc+Uu7JpVLuicLb2t5gba/SNsuMR8zNI6pDwFrW+5bldUt9sYaK6Il30Sp59cMSRx7OhZJHLs+T/qzPHLTH0StJu0LQs2Qviiuf2v8rAeabShS3qWrpbrN9dcmmgdCxMsUu66NeIPPIC2Vym36m0y1h/GUJY/jvBxQuzd7x+AEoaqMjh97toYPBefSSdrHBUU9mLrJNyj8UufQI7AFTo9fu+j74yHP2SvHwrVucXLqE1e3/TT26gjoDc+MR7JzB8QX4/DZ27xDe/JyuOjP7n2gufOook+Uly/KyYv6sueGoY8vBR5rlRcviqcJWYNWcWu9g1Rpll6y5xJoGyCv1DKVOUWqNrRcYu48xK2b2iTv03FJf9oWyFGn52gjeRI88AHajJ7edwC0BekzAsznvgrecg/Z0eqW0vU/N0mo70SsfY6HPoX1eCTDPbaxEcaxJ7/w82aDnrXNe2t7ruReolm1x57lUsTjJ85bpliH9ubNpgA4e45JMUfd4nksXAZTKaBelvFDFglY+lZ1mbMLrtZ6GidNIiHsQiPXhzWvWrdacHhxgtWb/6RP2njzlwZ07XPv8xyirOLp4hVOuoj66DmoNdoadncGbnzQUjjiesopLv6nYvY8LoM5gdujb+SDCWu+x1nsYtaA+W3C6t/BR4MwEPimW1PYC2ItyJYYT1Ar0GrjhZIfRIxe0SpQcClpFCxAPyUHQ0Co5sE+RIELDk+d68k3olbh9JL3i+rJsSq+4frsplqn2SoJ5n51X1ZJbl3e+zUDoVE+6byai52W5muV50y2xfeahh6DoVA890DDOU3ccOuSB0YZ2CUlG2oSbgYpBTOXQvYmXmtRTT0C9dC76Y59eh717UNU1t37rRzy4dYvjS5c5vnQZgPlyRVXXLE5PqB/f5ejyNY4uOQpGrXfg4Q04eATzlVefWA4+tFz4tMbOnO68Xmisdt8yuCxrvcfRzp2Bf7xtlnbpWm1WHBw+jPe11Y3aJQLFJKBcrdJ441rZOENQ7olvAuRhvzi2ImhvTq9oNZAQVADy81hftucmFM5WwFwp9YeB/xJ37fxVa+2fH9pnise9De9c2tTiW+cNhI45BmRqkg2Os4mypXT8pDRuT8zhvHRLDvKydG6QLE4F9OCJh3ro+DYRpD3t4iZiCHVXHC2TcOSBepHURnz3oG5s442HbeK6fPRt2HkMqoZqveb6px9zdOUKj2++DcDZ3gVWi12Orlzj4PE9znYvoIzh4Ml9lju7nHENnl13LvHikIsfHYOd8+TqDqu9BfVs7oH8+djB4afM6hPcL2lZXq+x+yZOuBxK10paRQY6gQTIOzM7B4A8mOTO+0H7xdMr27BSktBYigW2AOZKqQr4K8C/A3wC/FOl1P9irf1gSj/b4M1ftD2PQOgm3PmUui/p+MeDeykztOnb0S15rZixdEseEJWSRbkezumh26YGeZMx6jx2PNBELj146bYgYwyqFy2oF5uBOlDvaj77PZaDzyw7T2B5AEe3n6DvXsPoXR6/+Xbc5fDKjfh5ubNHPZuJLzmD0ys8ffMKAKquWZwdM1ufUJkVytQcXrrV+v+mmq5XzFanVOaMWX3MvD71X8di53D8nVWLVskDnZJakUAuVSlDQA6Qe9Q5veLWT6NX8v46fwd5jA4wPa+CZYxN9fy34Zn/AvADa+2PAJRS/z3wi8AgmPfKCxk3N2ifJRrnHg8zPe749P4xfYwtOzuVO4/bRnLn+dg6ufSCd56Ptwu85bFLdEsYccqVC/4cSA/ZSBb7PPSgO9fKSRgr4aHjdefG2lgeIA7DEuumGOVnE7KeYvE0S1MCwDbgHTMpw4D8PKTeM1dR2+1qfj97V/PMDzMce+fokMXpMc+u3WjE8t7O9h1nPaufUl86A73i4MOK1fyA04N9rNbsHT5jvn6KnbmnhJ17zzjdvczJ/lVMtUCZNYv6CdZW1HqHutppOHNr0faMqj5jtjyDxSkn7x2xd9ey58sHmBmxllZ92XD83SXVwrRAXAnAjt63agc6N/XI2+sb0EwLaLWlicGm0CtDmvLzSBGTfiZw5WNvANsA89vAx2L5E+DfyBsppX4J+CWAd26XHw1fNVXLpoHQIRsN9oXjnzcrtM9KyURDmaENeFMIkEpVTDt5aMhDdzbsoQePO5lblMZrd+9+GjotPHLV0C0hY9TEmYcy6gUX60089bgQBpVx6gLUCW9Gocyc2eqYi48fsF7scHLRceh7h4/ZOT3i5MJlzvYOWFcHUBvU4oj9o0N2Ht7j5Noe9+58g/Vsxu6hZX3gvqxSsHf6mN2Tx5wtLnB64Spn8+tga2b1GTsnT1icnVLVpyzfOOPofYMxsNIWu3BPUIcXLbay7H9coWunRT/69orV23Uxk7Mv0HkeIG/Ox808ctluE3oltusIem5qYyoj9h1jKEt0G2BeQpTWKK21vwz8MsDP/WuLyYj9MlQt57HzBEL7kojGHXszZUtueTB0DN1SCpA2/ZS58r6AqLOcg7dhbS/lUilLDYl0UfLoxjbzehojOXVcp1rIGIMJTz1WHewDdYgJR+4O4wKWs9UKDJxeOIi7nRxccfXR73/K7tldnty6CieXsadXuH/7iEuLh1S1K641q1cuN+nRmqc/MWN+5DJD9RL2zo7YPTuirjTKGrT/oc6uWA7fsqyuuN/dah8Y8Lw32nLyzTWn31o7JU5F5ok78AYS/bhbTgOdmwB5cx51SxCHAp7N+vHqFdmf60fs+wI05eWSAtOd2m2A+SeADJ2/A3y2hX43TiA6r6qlNPVa3zGaPjajYuL+Be68P2DazZ2fR6pYSvVPj5vSLUAE74Qzl/RKqboiCMqli4YJ5n6ZNVW2Npz4zXc1VsXJL8IhAu2ifMp7oF2sdRmQqgplat04mmnUbNR5B/8wOO5uEmnVbI+0S+DW/VdUToly5ddh8eWCu+9DtVqigRsff8jphQPO9vc523fA/uSN276jJ3D5HqwX2KcHPLrZXGba1KAVZr/i6Guu4NXiCegzuPC5+xozHzCw2vLkW4blG9YNXrsv4ebwdPx3VDUGwJs5AAfaunEJ0kFq6Nvm07xFqsG3C5mdXR75WAliZy2WjKLZlF7pCno+T668pJKZwrFvA8z/KfBNpdT7wKfAvw/8yS3027KEThnJm/fZ5GnfugKF5wyETqmcmB8vjm1CMLS730Idl4J33qduyfnzdIypJ961vstDj5NYQMqhi/V92aIl2oWwznvYWkgYnbfu+giadWVVFLREUl3ZuE8iaQwvBTf+Mezeg5MDJ/+bLV0lq8XyjMXyDPPkPs/eUTz72j58+a476Mll9wJgBcaATzp6ePNr7D99yP7hQ3bvLbn6G+L3qCxn1xR6CfWe5ehdw+qq98IDeEMZxJWQF0rwFl43ENPyx3jj8j+ENpA35890j7wr4JnvH97PQ688D668z0p69D47N5hba9dKqT8D/G2cM/3XrbX/auz+L1ON8iJtLMiOCYTCdrjzqVLF89AtydgF3ZLcADpomNzT7+LQJWce1pUAPdAuQe0SpYn4arcenGPlRf8eXgSvHlJQtxHb42eA+RPYvQ/aKFa7rpzs4mQJ2mI1mDk8ew+evW9BHcHXP4DjA7j3NqqeYasV1fIEqv3k3Di+dI3ji1fZeXTIavGQxcmxA9Ia9D3L5/92jZ2TeOF48G2BOA2lUgLxXKkyFsgjkBK8/LJqRQJ5PI8KNErJY+5cT1mfntsYeuU8mvK+yohjkoTGVlTcis7cWvs3gb+5jb6ed+Gt3LMcU3yrlMTTbjO9zvlgxmiBahlD5YzJCgVG0S1jjjOGbpHJQDl/Hjxxtz8kMNxBuZRULqiGOpE8ekjvD80l7dL8Zf7xX1AvVskys9bPCNS8lyZGVthYFsDRMYrFoY1Kkic3XTGre3fucPHhI9h7yr3fJ74/rj8uPoP9H2Dv3kIdXma1v+L6xz/myfU7rBc77B0+4Wx3HzObc3bhImcXLjI7O+XKvS/YOT0BYO+e5eRrNgVviN6yEvx3+d3E32wMiAPMwj4ZVSI9dLm+pFqBBsgjmHZ46l168q7StmH/qfSKPIbrq98r77NNC2p9JdL5N5Uo9vXzvAOcvePoAPy4XXLjIwOlU7jzdL9+qeKQ9XnnQ3RLAPmS/rwUEJXfZxMPPWxXyqbSRWjqptCmXfxBPIiHi9t570rZCOrSUwciDSO9dXD3GYf/CoVlfYWWJGC9WHD/a3dQdg33H8KVh7BY+cGGH2INtz/GPnsKX7zNg1tfBzSLk2dcOP0Mc6dm/mDB7N4FlrsXWO7tsdzdc2BunYce5tsMOnoH7GXw7vLEXZsAVt3eeOgj/Cd5oDNfL8+XsR559/qSmmUavdL0uxm9kvSxAVdeGsMUeyXAPLfnOTcotL3zMTY1a3Rb1i9d3C53PlZ7XpQu9twsSvrzJMs0C4iWJIvtsrnQ6aFTli7SHCVRu4T1gUtH2aS+S9jf0IC3BHVJwQTteqRhgPU1WL5hWdxrxvf2b3yfk8sH3P/OVdSDG/DgTTh4BlcfwMWn6fe5+sht+/QOHF1kuXeR+z9nYW5gfsbFD9dcePY0+f4KWL5lourErWzAGvpBHJqgZe6NN+vagc4EtIVHDgXQzqSDbZBPJYjD6xuPdxN6pUzVdN8s+o7fPtYwV16cL3QCCf1Kgnlu2y681WddVEvaZpiCOG8gdCx33uw7njvfpERucRy5t16kVkqcegPoYwOiEtDP46En3rg3K9Y3mhrnpUs+PbR1fQsOPVsOGaVho7KKB/9WzaV/1vSzumF59gtP0FefYJYzeHgdHl6Dj9+D2QquPYCrD1HBW99ZYb/2IXzvp93yD74Ftz9l9dZjljcUi3sa7SerMJXl5P0ae8mIjNcUtEvLEgADsLvl1BuHBpTyQGdcN+CR5xx5um18wFP2BcP0ihv7+EJa57FNufJNvHL4ioB5bmNVLWMlitvyrrsojE2qKQ6Nc0wBri7uXI51qlRxDN2SH6/MqXdniKaeeNd6aamHHo5rPPddYT04B1QT3Dpxt1izPKb3h8/BQxV8OjTUTSJj9MvNegCL3VU8+bld+A1g75j7f3QFVqEBtbOCW19g3/oCnl7CPLgOd2/C3ZvYS0/R1x/Apaeoeu6eDt7+FPv4Cnz0LvbpJR7/7o/Z/aJm78MKW8Hp19esbtUehFPwdu8kYC058dBOZyA/BOI5WBcLaw1w5M36cRLEsC5YSU9eAvLz2CYKlrhvoU0fVy5vAi+kNsumVqGozxEh3uiYqjsQ2rnPRO/8eVQ3HFuAawp3Xtz/HICeq1v6foeugGiXJz7WQwfKyUXiP5f7KWWTEcYbTzwOCagHTz0uW3FzUDaCuvtMa505dGn6+tKzRl0CjQcPcPUx+upj7NkC8+A69v4bmKeX3SxEVe33fwo3v8R++Rbms1vURxc4e+9DVu899d+LyI/nAB6+dzjeWBDPufGWWkWltEoXWMttcXnQ8+7O8Azbx3DiQ0HP80oRS8fqs7He/4tM59+KnYc+Gatq6e2jQ9XS1WbM+m0GQl8kd76plfjzXN3SpT8vKVzak1r4b2ZTsA6Wg3ayLexdoF2kpDGhieIRBZ8OLVCP+wlQd7RLAHbvsT9zYF5dfhr5amiomsT2zqje+Qz79mfYJ1eo797APrvkjvXZbaqbX1C9/Tn2ymPWv/U+69/8JtWbd5nd+QTtQb+lXlENH56DuFtX5sWhAf5823iwbnvNJY4c+gOepf5y6/LK5Tg3BfI+G1OvvLyf/I6bPzm8VDDv887zIOjzULW8rEDo8+DOx+jOtyFVHKJb+uqg5yDvLA2I9kkW6+DNo5P1qTUeeml7F+0SAqJaeNwKf5gMuKNqxbpM0rAuArs/llTQWKswTx0Yzy4/RVWmCOI2/+80cP0Rs+uPWP76tzBPL2GP91j/5rdQO6dUb95j5zvfZ/3FTdaf38Q8ucTON3/E7NKz5OvnapPghct1ubct9y0B/BCt4oZvE067TbtkoJkBeS5BLAF5KeC5bXolWJ+CpdW2AORjufIyz95/Q3kxLttIe5UG0/e41rQp/zElTmybVhW8md72PbKtvpOr00sZ8bjadVGVPal8/7LnVYkLv88jbAXQkvUCfOhYL16Kks664YtddUC/X5ys2I2v8i8FaCO+x3xNqHcSXsrz23Jd/kJZ9IVD9n7+X7DzzR+gFkvWH9/h9Nd+BlYzFnc+BRSn//InWX74Dtp6CiJkayaTKZN8nyajM/3O8rt20Sqd/LgA3tb/sCWPvP/8HfDCN6RXiscYAe5jcWEqVx7slaFZStYnUZxCp/QFQsd459sLkJ4vEHoe7jwPhpbsvOqWdn/5E0C3/rwUg4iqF++hD3HrwRqqJA2MmoxOiWoXvz3uH44vxpLsm203OKovBE6N4MsB9v7fGXv/eIdn33XtL/69BYd/cBlLzP7/7b15kCVZfd/7OXn3Wm8tXVXd1Xv3TE/P3jPDDNsw7AxCAgNGEnoE0pP0EDJ6YUvPCiSNDVLYhPSEnx7xLDvChEDGGARGGGEWAQKGGWCYfV9636url9r3u573R9atypt5MvPkcpce7jfmTvXNPMsvz8385i+/5/c7CZvesRUbTwLr+2QhQ6J7mUSyQmLLNKkt01RXcpQubaF0eQtMJRFpc5mA4sQ45bk83dceJ722RvrpDIl5g8rWMuVb15A93nIKlr92EjeP3Unutb+qKBM/jdyeFFTbp5oItUPllcdN5FbovdDC30lya18FnXJtTeZ2xLHGuXf7YZbPjT4RGiaJSAUv7TxoPVdbQ0S3+PVrJXT7hKh6nRhTitk4wnVCd662CFYZx07oYNHMFfvXBZ3NsjatXkXq5vdNbT11IknXQxlEeXNMMseTYEhW3lh0tG2FleClBFlIYwzN1BFuonuF1N4zsPsspakhChdHqRTN9V+qy90sPnUT+cuXSU5NY0iBMZ0gdSRN8VfmkX3+JF77bn8ScosfdyNy9ZOUu0cedMIziIccBl6etFeCUBStPKg0dFWRuR2hJzuFl66ss4Z5C187p9Sko2nn9dvcQxWBQNEt69aZf1zS/VW2WEm7TicHVw3dPWwR6nR01f7azWRdlqi7GYl6PR0s0TDrRWra+KaWvqmtZx9LI8qCqiXDSJQFmSMp1u5ZgxR1dd1QLaRBGiSyqyQTTpfGSEBy62VyWy9TWc6xNjlG4dIWZCXJ3MgYq919DE1MkCqVkAVIPpyj+rYls66mJ17bV9vu5o177/fWyGv73EIQ1TKdt07eLK98w54ma+WbdVuMhMMLjdCWpak4DkxHN48C3x8xwI+so8HVLSTkcVLqaIVR4DVZZXp01qQOdxvsGrqKNOr7q1q0XKfOu6H/KsqoNHOVrm4tlzCqiCXzTKxx9eDERfMfAhIFgSGc4+VLAAAgAElEQVTAEJAw5MZHCOenumYu0JXsWtuoY61rLZvuXabv2hMM3fIYg5MXSK+uUuju4uLevVSFQCAwzqU9j2/j90CtjXvJKvb9qt+h9vsF9cid50tjiFzVv1dCkhcarZXX0PaeeVyp/a2OatHJGlW14aede7aj8M6Dhji6IWh0i5cn7tqHj4fuJ8eob8b10TNWDb1m04b3qdLTpXNpAOs+c2wsMs62MuJ4ikSlyu6nnt9sKimhp7oRPmhFQrGtVFwn89yaQ+Kwwrov1VUiNTdL78wchWyWUjaDqF1L2U0ZRJUBah6fh6fu4jnby3h55M7yKpJ3J/JGwmv9FZWk0yitvK6+z42jJWRuP1ftIYqNWHgrLOqliHgSiHQyPqO8vMLar1cikeoY7ccUVW7xI/QNWGQYE5vSiIq0VZOibnKMExbZZb3Mpm6/ORYbQpGlLeV+l3GsSkH1tSskzvQjy5aFuJKS4utWSSTVZ6cjPBGQq2lAksqtbqxHXoOD0Gv/SIPcW4STaTJra2TWzBc0k6wiblsBFUkr5BTlXxeyVevn6hDD+noqkvcm8mZ45TpQEXlcWnkQ0m+5zKKDhMp9WUeQA6gfRNsFYd0X5q7pciK4PYZFXVTHzwYdjc7P29hsqzFyiy7cJBerDFALA3SQi4/soirjKj/4yC9KCWa4QvkDc1SvKSJ7KlS3lSi9cwluKjjK1j4Jo7rxSZ0XdP9NF+KJXpKFEtkfpDGqaplHFVIo37wIO4rIhIR0FRISbl5F3LRS3y9Si8itIYd2WcWNyN1+TzeP3CsEsRlEHjUUsdlaeQ1tL7Oo0OioFu++45kIdUOYJCLd9c690vxV27TsjUlucd/uTCqyyypuNm204SO7AI4kI6tNOvKLrTWzXO0fwxWq71za2FcjXT+ZSVwxyH6pG1ESlEcyJNeKpI6mMZYFxXevWo7Xw1PPSMS752DeMPX7oTIip44uieKNq8uF88hbCTW5u0s7Xtp2nPkmTXnTUDug0VEtOvquV30rVCSkI7XEEXcOm4TulanpdTyNklvCErq7rGKPprHvt0NN6jryiyHqwyKta7bUL0lQL6HUaeuKcU/+LA3m+5spZdN0zS0iyoLEkRTJ5RXoddfL7e0bA2UYWP+3B4Fb/x2FxK3lVUTuvq8xHnndtgDyitc7RP086419PrKJ38Sn7hN7y2QWwyad2KNaoiDuqBbPvjQiSrRmvBsgYdRP0HhpeO6z9LqPn35wPuYGu1hVWaJ1222k4LfflZAs/ejKL9byKhnGTZLxkmcMITGuJBBSMD8ySCWdIr1a07wlxryh14ZN+rBGpigzN62fujGIj8hbATcirysT8vxutVa+aUebolGG2QepbsLFYwDr78zxnJBu7dSdHGHu5AG1c2s5lQeic3JvXrxqD0m1rZ0JXaWnKzVkG6HW6tjruRLm+nYVwcttZebGhriybwddswv0X5wyB7IsEENlNWG7ELiVxFXH40Xibtp4WCJvlleuA52Ycr9tG/sU106c8Duuq0ZmiRKiGEdUi3ZfESJb/NAI7Tyo3LJZxpn67ye3RIGO5KLSyb32A66yy0ZGKmxILzXd3Z5Faq1TFzZoLxLw4XNu7zCzme10zcyz9egZhJTIlETeXIBuqbTB7pB4hTHaSdJa3y3U0L18+xG536SnCkFDEVXw08oD5Y8EYK6WkrkhxMaqc0CkEMWwa7U4bGJT//TUoRswEaq7WqJXvaDaeb29/pOhSq1cYzy99HNAEZpI3fYgk6IqQjdRr6P7T47WUE/qhlDnJdhvgvbzMYFUhh1a+65ivtBi9sQeZif20pO/zMjkWUgkIVNFvHIV8ZpVZXy6l2Zu/64iZHO78wmtmSQOwYlcBR0i10sY8iZyryVum6WV13DVeObg9M6bEdUSOf0+QmSLqo0wXq4q7twPKu88THQL+BN6kGPQIfR1S8w/6+eADulbj7t2Edd74dX1bcYGWagSj9xg99yt2FwCQDJzbD+zp3bTu+0Coze+iLirvqxbGzX7db+rSNxaRknoLiQN/kSugzBE7heGqEJQeUXZhqYME8caLDpl2lYzD4OwB6MbFuV1oQZZvN6rrtuP1mzt3Kzv9Erc+lB6PAFOUq/H66AautJODx3dqRP7p6O7TZR66tcumjPUCFoydeRaZk/tpn/HOcZuemHjhcx2Xd6rPV0d3XEsHm1Zx1B1Heh45NY4cvtvAO5E7gWv6JXNcYomr1gRdDGtoIgyH3dVeeZBEeQNRLqvlLN6rHF43V5wk1qiaufWrFDAEaqou0wu+MstnotxATohi/XH5u6hA66hiV6yS7VO7rF05vsAY/UOqR9nW123eYhav5Wq4PKLB5k7t4OB3WcYue6IUkqx1tHdZyc4lRdu/be79666YbsTvVsZ676gGrnZnr8HHiQ5SAVdeaWuzwZp5boTui33zP1CFJsV1RI3dMIUdU6sILqZX2iT3+Oj2rt3ntTecbmqx+8gj7/hPfT6Y/H3wFWLeLnpwkpP1eZdqzx2OxmqvHJZFVx87gbmzu1gaN9Jxg4eXn+BhHsEiao9u+etjkpRL4alS+S1Nmqetn2crGNRN8Yu0TEQzCMPMuHpBbV2rvf06heKGFUrd7XBh7NaTuZB4ZXa74cgB1uXbOAxiHrySrAbh47UEjUu3e/RMGhYVtB4dM+L0sMrc/brlFy8yHqjnqVMbRkAO/Hb2wtK6ipitxOkkDDxzE3MT4wzcu1Rtl531JPIlaTu2n7V9bg8j8f1mJ2TfSpZxcsjt8OLyKNMeNbZG4O8orRdYWvd/pDXa1iyv+rI3I6EfxGPuvF657Gu6RLjj++nnfvX19Mhg5C3apuOx24l+igeutMWJxm5lXXTo9Wacz2h1toykFARnHvyVhYmt7L1usOMXXPCQcw6n027qur+YiBxFUEH09DrxxV8POEAE54q6ESvqOt5E3SciJokZEckMhdCvE8I8YIQoiqEuCO0EQGlliALb6mWE3WDbvaW52OgC7nV3aU1JkKtcEsiCqTB+UzcqAjdzzv3jghQEYHHJJV9ImudTNSk7e69bZCZi4fuJ7volN34uMgV7kRvIdoqnHniEAuXRhm/8XlG959wkHHwj55HX/fxPJ56EndOYDrL+k10qp667P16rrWvmPB0C0Osq+dJ7t7nua5Wbr+J6tdXX/dByT6qZ/488B7gwYjtREI7eef6/YYndN+2fU4CtzR/7/Ul9B4ptSeYAmqeQTR0qx1uRG0/riCkbrVXN5LFuk1WDE4++goWr2xh5y3PsGX3GddxUsFXdlE+Iah1dfs42I9ZpY3XjZvCa6+31fnbeC5cpfDIw0x4mm25P7Gpt6meMPS18vrjUN2I/OWTKCunRopmkVK+BCAi6NiNgFfkSjOjWsxy+rHZTlvCLcCl04/uiyis5azH7GW71zF7xZ+rytWPs36Ui9UO6+9oj0ev2vqwlwVwvPxifbu1DlAXq16333Lhl0tJjj98F8tzeXYfeprB7RPKcQoCtydFL89WVaZ+0tpWzmOS01reK2IF9DRy5bF43PxV8HparN/mbmN9/+qxaZRW7taeF5oWmiiE+BDwIYAd41F86eCwJxAFyRatu7g9SDtKRigEJ3S1rd5p+m79uK2qCKy/AMM9M9TapjK1n83VFgFHQpH9OL1CFq391rZZidP+0gu3lHw7SddGb6OO5eJRZ5BSV2cD9mvO9lOXiimOPvQqVhf62Hf7kwxsmyQOeMl+6rhrd/nNba2iMCRuraeaYPQieT/S1p3wjEteUSFsKKKOfBImwMGXzIUQ3wfGFLvuk1J+XbcjKeWngU8DHLolLR2p+wFT++N6nVyzoZNR6hq/biVrjTJB+tSFiljd+lKR/EY5UR9/bt2mLOfjodf+7fskofDSrbaqvG6Vp16rY5Z1euyyAqUXs1Qm0ySGy4hryxx+7NWsLXWz/87HGBi7pDfgAeHmrdoJX5fE7XW9JBV7u2GJvK49jwlzVb9+80SNkFd0pUVHHwGJ3CvAADTIXEr5Zg27Wo4gr5Nz1g2w2FUdWfmv/22WC7b4VlC4yjGW7UpCtfQfZN0WP7lF9wlERegb5RQkr+5Xj9DrZBUfQq/VM8tveuq6pM6qYP4/jlFZSEJBUO5OMnFwP+WuNAfueoT8yJW69sLCS2awHkP9tmgk7lVHl8jr+vdICqq300nkOtEsZh/e80Ze24LIK662RNDKg9wcWpoB2kjv3FnWe62Weh1ab/2SOKCSK5z2qDM+dbRz9aqIau3c7wXQunKLqi9VxmhdOYt+Drh67RsXvWIBLrO/TUJX73eXXVjfsvEvm6fuLr/USzZL/zhIZSYJFYNSJsXEdfspp5LsvPISg6OXle1Fgbtm7kIQLnq4qr2wJA7eHrkbyeuStteEZ1055cS8903HL2VfJ/EvyBoscRC52U4ECCHeLYQ4D7wK+JYQ4rtR2osKuxLvdXBhE4gc++p+ZK9y4R7FwkDn5PB7ZAsSe+43CeQZKqapjbrZYQ9xc7PNGfGxSRqqePNaGZ1Illq92mft6W6oGFQNg/M3XUMllWT8+ROkj5SQJVHXXhwf+7iqQuSs9rkdQ/0Y1rcRlsjdfhdlHR+P3DvaSe/cDrL2StjIEp024pZYzL4iQEr5NSnldillRko5KqV8W5T2Go24Ys4966FH7m5w96aCnRSBQhkDhCr6XQy6npK1rJ8X4zeJp3w89vEQ7baqiFlZzoXU3W/45nYh60lS5+L0gyrW3AoVgVttdj0mG4mrMz6diUlgjrU6VNTn5q9L2ooJz7pja6bT1MS+dHDVZ4BGQSPS+3URVxJRXXmNG4HW8gM+HotuMpEVviTvczFbt9lXWrT27+eh27e7EbrZl9pLt/djrW8gyR1agkQVo1pl+3PHMcplJm7cR/m6BCLlbDPsxzmG0pfA/Ujcyxu3JwG5jUNtu+rfqt8p3M08uNPgZl+coYjubajt1dLTNW/8bUfmcWaDBkXYmWiv0LAg0oZffdcZdo1JIZ00/6ip/lHkFrf23S5qe6aovX8robt5jXZJwRBVB+nZydFOpiq5I/+OaZJbSohMlVSxyI4jR0lUypzdcpDl2byDdOP6WMdJlfKvkmfsx2Ntz1nfXXaqja3zBuHtsYe7iTvP/bpjUD39ufXP5tNhWK28vnx0rdx+DLpoOZnH+SJns71g8BqAONcp9oPuqoRBEEU7b4XcYvard3Hbt/vZ5eWle3nqfvKLyktNdlXY+odnGfzARfrePsPIuye4/Rd/QDpb4Nmf3M3izIDD7ihQEbfdJpUHriOnWOtY29yo5+YE+NxkzT5b65G7IczythCfVu5axkc6bTmZNxpB12oJK6E0ayI0Lu087HE2Sm4J66Fv1vcnDy8S8pIbgpI6mG+/675xmfxbZui6dYlc7yq33v0A6UyBZ35yN4vTA0oPOszHbSzcJket8J8UVWvjtTG09+lXZrNfn9/T96Yd4InP9RrQl1fc0KqltJVlG2iHNhxSSkSpJUhUi69tHt6KZz1Njd2VhDVIP4p27t6Xm2YaTm6xPvr6rd+ivCgDPH5b7XCXVNTygGqfLqmrJBiVJNHVvcJt99xPOrvGMz+9m4WZQS1P0TEmNrnELbrFTWN32O0ip7hp495j5k3kjt9LJaMo5TT1PIG/p+5/Iwoir9S3rSGBBtTKo8iyLSFzEbO0EhRBolrsiHsi1ArvJUE1JlkCnlx17Wh4MkHkljgmRMNo6N521JNOEOnFi9TN/l0mHm3EmM2tcdvrfkQmu8bTP7mbuakhDCERmB8/ovYi/6CRLWpZpmr77j1OfuVcJ0jdnio0PPI4Jzz9pBH7tRCEYMOk5Lu2pRGd9rJ+bZwugqzV4tmOiJYRapbzzwoNsl6LZzvUZ2qq7HJLoPJLJtLpU9Vf7WJxSyqy9+26XaiXHbD/Rm7lavtMW1zS99cJxJ7Jac8QtR9bV9cKt9/zQ5544A08/ZO72bP2POLxKlQEmX2rDL7vCqnRktsQ1rXlBdeUex8t2vxuu1k5SM3fG6+3Jfx2t2MNK68o29KQV9wckKBaedzS52a7HTgQx/oKccDrgm20du4mt/jZoOOd665oZ+/D1ROP4KGrynkRl/ld7al7eev2Mczm1rj9dfeTWCtxwriZ1a5ekILCiRyXPrUduayWbdzkBmufogDFo1kK5zNYE6TdPPEgRO4lq9jbcN3n4pEHmfBslLzihriCEuyI8qRsR9t65lFT++1rtfh53177g6T313t6mmuURCyn8+Jn+3bA17tXedzWl0C7lXX3ir09cTevXcsT9/DQzfadKf617fZyNbtrsJavr1O1bKv31je2W34vO6Enpqtsf+4Y5647wMSN+xg9epbM0ipJWWDhoX4G3jqrrOeF+Qf6mfmHLZCQUBUk8yW2feQ8qaHyRhmdKA//G5o34W9sj3Qz1idyd+89mLzSKq08DrQNmdvJuuH9BVirxQ4rcfj2Y2lHfwnd4Atw6azZ4kr6GhJQULnFS76o9QkoFv+Kj9ABLdkF3EldZb+qjIrYazZZYT1vSpcyJMsltj97jImb93Px4J6NfWK+SuZbq6Sza2QyBdLZNdKZNTLZNdLr3zPr29KZIkJICsezzHx9C7JkwLpKU7qS5sJ/2s7uj51ElZKh8p6DELlXWb+IFc/tIT1ylU1u28z+/Yk8SEy513YvRM1HgRaSubFOLUEQ1TuPAi/vPM4lZn3tcCHqONuNQuh+cGvb7QkkCqE7+5AOz1tHS1eVr5WBelKv2WxuVxyn5fzNjK2BFCRLZXY8dZTVvm4qqSSVXILUtWXECBQLGQprWRbm8xTXMkipyqSQpDMFjJUy4roqyWKZRKnEwMQVUmtFynMpCuczZHcU6uy2w4/E7du8pKsguQGe210J243g3W3y60sHUWTMMFp53dOEj7PbNp45KMjaJrVEhd9KimFfWuHYF/NEqGc5F89ba9VFGwm7LZMLODzruOQWV+IOQeiwudqiaZtQeujglFNUUopKWrHLL9Y27WXdPKzasWR3FMjsWKVwJodRhu65RRASI1dh9++eJNFdX19KKJdSFApZimtZCmtZCoUspXXCn3thgKKRZSXfSyWTIr1SID85hTAkciWh5YWrjieIBGMnykZKK87twXTyoF55lElPx74YtfIaWkrmYbzzZiKIxx3WO49TO/e0z0M/130jkVk+HrmlEYTuOAZN2cVum2q/m/wCihudi8e+uX/znN/xu2e58vVR5h/tR5YNug4sseW9lx1EbogqCEhkCmQyBeibd7Q7Mz/A9DdGmNy7h8UteXqvmJq7rAiyu1Yddjvt8iZxVV1dWSWwp67hkXvZ5bfdnYCjRZropO7HrZXX0FaeeSvgp53Xl41/IjRuhH0bkbKtmOQWtyeVRkkuQGDZxexLRxsPTuo1KMcgIxn95YuM/vJFpY1BMPjaWaYfGWFhZID8hSkS5TIiLdnyrkskcuq0e5Wdqm1+EowXQWlp5x71g4QmqmxT2VG/PZhNrdDKdW4mVx2ZNzuqpV0nQnW1cx1Cr/eq3d5fGlxuUZV3314/IRqG0E071Dp6bZ+u7GK10YvU3eqqjjFMtmcgZKF8bw6OC8aSZ+g5tMTg66fpvmbFUVSHwCE4iYfxyL0mNdtNXqmzzYNJgmZ7Ouvra+U1tB2ZN1o3j4q4JkKbpZ27lYlqW5zeObhMFmoSOqg9cbstfrKLaYe7x+0+4ane7kfucaNaMjh75hrGd5zh4K+85NjvFRNuh46WrquPe+3T9cgbQeRW6MorOl55o9drccNVmTTUyrVa7PBar6XhnlgIBE3zB6/HTf/HWZ2Lra6up7ei90iqSyrK/ZreqZtn65UsU0tIsn/CwFrfqFaRy4LTJ66hVEqz/8ALgexVta0qW1cmBiJ39htswtPLPq3+YpJXvBDmGgt7TrTcM9eZBG20dx4lqsXRVptMhOpo5w7bNeUWlYfppcO71Qk6Iero00VyMe3R89CV+zV1ca+JTpUM44awFy/A3MP9XPz7MSqrBifvvJne3AxDg1PKmHKVbV52KIk+6M1R0yMPGkuustdve5SYcu+2WquVb9rUhoh7jXOtPj26dD5qBRjgupPGPqmk54XqLsCl6/XoPHba67h5DkFWVjTb8Vq4SeexWrrvE+oV+dz2ee1X2Vqz1+5RWz1yP4/dr6wuDCFZeraHC1/YRmUxycLQEOVshr4Xprj4tVHP/nWPp65cwPFT7d9sX/P3tG1vprxi7z/UNRPq6TP4E/Jmf20Aoz3MqEMQi8IujRsEut6D7kmnU1+/js5kj9cFoEfouo/eUUlHh9RrdrtJErqE7UX0fjeBS98YQRZN62d3jJJaXqPr4iLT9w9B2d9uHflIOR4BvHH7/jAaucp+q82q7VHllTChiGHiyj3bDsgV7ceiIdFo3TyIdx52oa5GLeaj7NeD9F3XldAkZx0vyIvk9C9qPULXgYqAopK6vV5Ub9yO0nQKAJkwKPR10zW7aD7TSqisOjNF/W4+jvKKMYyTyLXnQDTOO93zMYy8EiYUsZla+WafVwn8XljRasQ1EapLZNrlNEOc4pRb6uraSNHLq2qlh64qYy1XT0r+kkUQcg/7ye1YBSRGpUrvxRkWtg5RyqQwUlWS3WVfe7w8cb+xCSy7BNDIdSNXdCY9gy6iZbfN3laUtH1HuQBauY6j17ZkHoaso3rnUV5aYYeuRxmknUZq5xDDpI6L3OK0obEeup+OHobUa2WdNrp73HFErXhh7N2XEGmz3+GTEwBMX7ONbf9skmRC3Z+nvS7joDNenu1okrXT1uAyXdDEIJV9cSKObE/9Sdk2gY5u3mzv3EH2EX5oL9IK224c2nmocKsQcov3o2bwG5aXp6fa77TNm4BqZXTkl80+vWWUuEMT+/Yuc+0fnKDn2iUyYpXh2QkWRoYxbnYmK/l5sn4EXStnRxAid9QNLbvonS96cl+4ayhMXHncSUJ2tA2ZtwpRvPMgUS2OupoSirNea3R17RPRi8wiTojaEYTQdT1KHcLyKmv2G0wfdyN5r08N3ftWuPYPT3Dr//c8r/vwj8hkVnnqqTuRUuPmEvB47WXi9Mi99+k9yUWe/Nd9um0zrbyGlsWZ29PuAUfMebPXOFfBL73fmgnpiF92idVWQTfF32GfiDfu3DteXDNrtW5M9OLP7THbXjHoUJ/2b9bT3L/+3W0ZAFUZazm3sjXYs1/dyMcee16cSXH5O0MsHesmM1Zg9N4punatKeu6tZ9JF7n55id47LHXcmFiJzt2nKkr63rzcbnGQhN9kJuszxOVbtKZjk7ubE/PWYkaiugoF+BpOIgE9LLzzIPq5vH37z0RKiVMvtTFmSd7KBfrbVudT3D60R5mz6VDe+fN1M7jllucNrp76FG1zSCTn3a4aerWOn7HafXei5dTHP7Yfq7cP8jqmRxzj/Zz7M/3svhct+8kqB379h2lv3+Wp566k3LZwJDu9njNDTSDyB3tN9gjb6a8ElYrjxLdFskzF0J8EvgloAicAP53KeWcbn2Vdx4U7eC9e8HqzV4+keMzv3kdS1NphGHa/N6/PMENb5vle/9hnJ9+ZiuJdJVK0WDn7Yv8yn8+Sbav6mhHB9UynHuin8Jikq2HlugaLHl7ycJjsS7hnxlq7tv0pj3XsBH1y+WC+0sirLA/DdifFEDfQ3c7ZtXiaSpPvVYWnC90ttdT1bVi4qujVFYF1MpIQbUoOPu5cW78D0c8szntMAzJbbc8zP0Pvp0f/cUbGTh1ma6dq+z6wDl696/U2e1nc127OnMMAYlcV1px2BginjwWBygGgnbui082FTICmQoh3gr8UEpZFkL83wBSyo/61bvtloz86Xe2AjjI3J7aryJqe2q/soztu70f+xuInOV99lsuYDtp2S/uCoJKGT7x6jtYnEqBpXwqW+FN/+ocP/jUOCVLbHAiXeWae+Z5/385qezT/G4w+XwPE8/00jVcZv/rZ0imJVeOd/Hl372J8ppJDpWSwV2/fY47f2ti3T7DvU0L6dSVs5GRtZ5dbqnU1bOPjbpNe7q/ndCd+92PwWmPkw0dZRRk60bSfouV6a6kWcOTv3cD5aUkpWya03fdCAKShRKJcomhg9PkelbJZmufNbpzyxvfk8myg+xPfHoXzxTuZLW3h70PPUeiXMFIV7jpY0fIbXNKN0HklzAkbi8TVlqx77PbE4e84t6ez41Ks6zX06yOHHXn7rNPSCnvQIFInrmU8nuWrw8D/zxKeyroeN6t9s7tXqjKuzv+0zzFFQOkoDjYz+J1uwEQhuR/PHYzpds2ibz7+Dmyl6Y59kA/q/MJcv3Ol99VSoKv/P71nH20n2oVEilJIr2X93/meb7ykRtZmU6BxYZHP7udrbcssuOOhXrbdXV2D89dVz937lO/0MJs091Dd7RjOwYvD961jIdOruup2+up6irt76pQXkoyu3OMatIgP3GFcjpFJZNkYWmAy9PbKBYz6rqJMtnsKrnsCtnsGmljjfmpXpKJItXBJFN7tzF69BzVsmDi26Ps/+1NHT0WDT2CN67ery8vNlNe8UKjtXJdxDkB+pvAl912CiE+BHwIYMe4u3LdqoW3nOuiey++FXRyc3l2c6iX940z85pbXMsnl1bJXprGSEiKS4LZcz08+ZURVheSHHjLDAffOs2TX9nKmUf7Ka+ZY1kpglyR/N2/vo2F7kGWB/oo9XeDlPQfOQuLyzz792MOMnfYGrPcYtYLPiEK9YTu3OdN2Kr9gGcZ+zFulPMhdQhH7FKaEkvxSopK0mBufAt9F2cYPXwGkaoyeMc8+9551my/YrBWyLG2lmVtNWf+e/3v6vrf5ZVuriyNUNiZpeauL44OMnr0HFQNVs7nHHa72WqHTshh4PBQHyLXnfB02hpcXgmCRmvlQfZZ4UvmQojvA2OKXfdJKb++XuY+oAx8wa0dKciAc0MAACAASURBVOWngU+DKbNoWbeOVnveOvDzzve8YoFKybzg84+9SGp2kal7bqM02E9+5jx933qWzOUZhBBIKSGRJJGucOT+If7p/9lDpSiQVYNjDwzyxJfGWFvMUl4zf+aL99zG2tggxb4eZMryk1bNMZu+7Tq6z10iV36WavUYhqH3piHzOKJHt4Cp4U+/0E21Ihi+cRmRVq9o6LbCompfaV5w4Yd5iosJhm5dZuCmVarCm6wdx+dC6BBMI/fz1q31a5j8zjCXvjOMLAvmdo4ikwkGzkyCIek7uMju3zi/2X6iSnfXMt1dy56kW1pI8sS/vpGySFNJJzEq6+RiSHp2LUeWVCAckQf1yHUnPMFbXvHq06tN3X26Xrlzn/5EsC4iaeYAQohfBz4MvElK6XyliQJWzRycejb4a+ftppub5b2186/9+z088nejFFdMbzrZVaX8+r2cve4OCokuel88xfBPnya1aA5jLl+kXMhQLtYTRCpXITsAS1cyVDIpjv3Wu8hMzdE1cYXM8gLppRWS06ukllYoZzPMXb+b+YO7KXflGOqd4XUHf8arDzxGd27zvZBe2rl5LG5at59ebXDl2W4e/JN9VEoCzP+462Nn2PqqRdf+/DT0S0/18sS/2YmUUC0IElnJ0KFlDv3peUQinI6uKqeyra68xtOZW/0nf+96SvMpirk0Z+66gczSCjseP0Kiq8wr/ssLyjo6OPG3O5l+ZIBqcfMJ2MhUuPVPXyQ3VtjcFkBOgfDeeBQi9/PIw+jkdpuCRHN5hSI2Qiu372+YZi6EuBf4KHCPLpE3CnF470GllqD4pftOs/fOBR76/BiF5QQ3/+IUr3z/Y/zFO05zeuftzN12gMUDO0msmhecqP1v3QZjrUj32Yt0n73ItsS5zR1A/0unGXzuONm+Evf8wVl+8Ml9VBCkVtbY9sIL3Fh4jGv+BB488mq+9ug7+Mbjb+O2fc9wz/UPs3vkLKIqefwL4zz7pa0UlxNsO7TAq/7lWQZ2qyfMdOQWgNKywf1/uJ/ySr209rOP7eLtXzxMbkvZ0abZrruHXq3AU3+2ncqa5aayJph+qpvJ+/vY9manlKQju6jK1WwDNSnbvXUpYelEjuXTXWS2FMnftEjCqD9rylWD2blBJkd2s3jDAIW+bqhKhk9cQADVlQSyCiJA4LCVSK759dNkhwpMfn+EymqCnr3L7P21cxtEHpTEQY+klW3G6JE7bNIkcj+b3NoMUs+rbJQF9IL0GVUz/2sgA/yTMB9vH5ZSfjhoI2FCFMPo5n7vBw0KrwQiFYSAG986w41vnQE2vc2uVIEtP3ma/DNHmTt0gEombZY3JEYCqmXzqi71dTN38zXM3nYdE5UyuYkpchen11uXSCkprcIN77jM2PVLPPPVMVZm0+x/wzTXvmWKREpyx7XPcWFmlAdfeiUPH72DR4/dzo6hCYZPH6fwzTmqy2ZrZ3+WZ/KZXn75i8/RO1bUHgc7GU78uH/jnrO4Y4SV0SGkIRAJ+Nq399G/v0BVCqQ0kFJQWf9brRpIzL9VKZCYMlNVCopLSeZfnTPrCEGiWKJ7cpqeiSuc/24/2968oK+Ru0yOmr9PMFKvFgUvfnIvi8e7kFIgDEmqt8yNHz9OKl/h0pUxzp7bw5lzu1la7oO9ktzsIlsOn6H30izp9Zt4dmvBQeRBtFiRgJ3vmmTnuybr7HNDUBIHNUlXy7A6nSbVVyaZq0Ymcq8QxEATlJrRK3YEyonQjD/3g6etPu1GllnC4PZbMvInFpkF/EMUwV9qUZax71fWqUejwxTr9kvBQ/99jH/8yz11oYlGosqO2xeZOtnDymx6s3wyQXHPEGv7xpgdHqc41A/A6P2Pk3/+BOmuMr/+d88zuG/zcdpNQlkrZnj0+CF++OxruLgwhlEo0X/0LP3HzpKZXSCRqHLDey/xmj84azmeYHLLS18Z4bHP7OLCbbewsG8cUa4gqlWQkmS6QipXQQiJYUiEqCKQm99Z32ZIBCAMc39lVbB0JmPO0iAp57IU+7sByBUWOXjoKHu2n2J8ZIJEoqoVmqg6Bq+yqjE48/ejTHxzlOq6LFY1DJa39FE80Mfi0CBrhRyGUWF863l2bj9FfnWKU58ap1oU1B7BjLTkut8/Sf4mU4JaOp7h4jf7Kc4kGXjFMiNvWSCR9b5mddfXDyKnbNRxIehz3x7i+Oe2Ua0AVcG2N85w/e+cx0hJZZtBiNxuq1PecJdlGiGvBC6rKbH4zTMkkNy++1xjZJZWo91e9gz+E6EqT/CV77/I+Wd7efbbwxhJCVLQv7XAL3/qKIuX03z+t28yJ0CBarnK2979CEcfGOTM9/KUenKsjQ7RdfYiAJWyQddwqd4mFykkmy7wuusfZufyYb7yyddwZfd+Zq/fw+xN+xClMtmZeeaWr5A48gLbhy8wlr+Mkai/GKxyy/SpHM99bozpI90M7Fvlhg9eYm3PAMd/4Q2UcxmGnzrC8LMnEFKSzFZ47Z+fZPT2JaD+JgHeGnq1At/959dTnN88fYs9OVZ2DyNf1cczh2/hyRdvJ5UssmvbGfZsP8WO8TP0dC1v/i6aXnqtLKhJ3eqtX/rRENWi+bQwefM+FkcHkckERqnM7pFT7N59ku3bzpFMlTfqd923wrn/OcbK2Ry58TV2vOcifdeadl75YS8n//OISfZSsPhijovfynPTX50j2WUltwCP/yG8cDDHZuF4F8c+t52FE92kesrsetckO99xmSsP93P0s9uoFjadkQv3DyAMyU0fOatoqzFE7oew8kqksgFujFHRtp45hPPOW+2Zm+WDe+cA02eynH2+l/6tBXYeWkSI9YSjkuDUI/0UlpLsunOBroEyJx7K8+X/8yClNUuiUabC/nvmeM//e3S9Xb3koLnJHJ9/361UignKuQxL20cpDPezNtRHaaSPsmE+GSSMMlsHLzE+NMn24QuMD11gdPAK6WSJKy92848fObARdVNNCq7cdZCZ6/bRU55j9AfPkJ40iTuRrTB62yKv/fNTGwkvQcgc4Mqz3Tzyx7tBQrUkMJIw8uoFbv2TCcqVJGcmd3Hy/F5Ond/D0kovACODl9i1/TS7t59idOgShiG9ve6AnvpDv3MTpYUU1YTBqdfeQqk7S9fUHDuefolX/vVzpHr0Rb1qUfDIB/ZRXbVF1KSr7PjVaba/bxYwNXpTojL/VqVJ/KZ0tfkxoO77prRl1hNI23aznFjfv3I5zdG/3Um1nDBz3oQwwydvXWTpVIbVKxlzW7VK74UpjEoVI13lLV98uu5JIgqRQ3iv3E9eCeuV28sHyWoNsmZN7buXZ942ZA7xSC1XQ1SLG5m7tuciYTz11RG++8m9VCuCallw4I3T/MK/P0kqp/YkvQj9H/7ges491k/F4l0lsxXe+1+fozrYzZmp7Zyf2sr56W1MTG1juWDKGkJUGemfQh5fhhMrZKfmEVIy+dqbKeZ7GTt3lA/f9xUu/qyH498aploW7Ll3hp1vnMVIeGeI2m00j8ESmrhkMPFAnuJCguFDy+QPrDpIv1I1mJod5tTEHk6d38Pkla1IaZDNrLBr3PTad247Qzpd/zTjNW519lrsO/rZ7Vz84TCyYlBJJrh0/R4Wtm+he2Wed7z/m/T1esf4W7F4OMsLHx+nspJgcdswF+68HmkIc+LFEJAwSbYdsfNHT9E9NY+RrvD6T79AdriknJCMQuR+E57NkFfs5YPMEYQhcriKyRyChygqy2j000xCj4vMwcwEnbmQpWugRLavEijt3UqU5TWD+/9qL4e/PUK1LBjYtco9f3SSbYcWHWWlhJnlASY2yH0rR17aTbk7t1EmubTKth8/TffkFf63B57CsAh6uun+9n7tdc3jcxKtKgqmNg5rhQynJ3ZzcmIPZyZ2s1bIIUSVrVsm2b39FDvHzzCUn1auh+JH6qXFBE/+m+soLSSprCUw0hUWtg5z+ZY9SASvfsWP6Tl5hfNfH6O0kKR79yp7PnCBvmudgWAr59I88/s7qRYMij05zr7uVkq9XRjFMqNLZxh53RyGMOcXEqICwiQEsb5t81PbBuVyklIpRamcolhKUyqlKZZS63/N76WSua9cSbkeK8Dw4bP0XZgikSmzfN0QFwb3YpQqjD19jL6zlxBAqrfMm//7M4hEYz1ye31f7dlTtoknFNFuR1StvIa2JPOHvjOu9rwbsFaLSrW6mrzzoDHTdfqyR1lVVEa5bFApG6SyzolDt3VbAD7/9ttYWu1mbaifUk+OvlOTJIolkrkKv/aDp5B2ko5A6Pb65nF6r+VilrHVqQouTG3l9PndnJrYw9TMCAA93QvsGj/D7vHTbB87R8qicV95vJsTf7OF1Yk0meEyuz84xegbLPHyRcGlnw2xcKyb3NgaY6+boWDkuP+nb+LCpe30Xp5i7OmTJEpmm0a6wq1/dozePavY8fi/2MPK+TRUBdVkgsk7rmNh1xiGKHP3Kx8kl12hUMiweKmbUjmD7DIoFDMUSxnzbzG9/jdDsZSO4MlLcuVlklfWSC+skl1YpvfiNJV0islD+1gaGaJ7aoatjx4mtWJGPhmZCjf8zjl2v/WKo7V2IXJ12x7ec8i4cruNQROsOmRuL+PTj1nPr47P/giEHsQ7D0LmfuW9koOUbbsQ+tP/bStPfnacik3DP/i+y9z+kQnPxbjMdpvrodeXM+suLXdzemI3p8/v4dzkTkrlNAmjzPjYeXaNnyY/d4mTf95PtWBZViBT5Zp/cYmt9zolFGtf5YLgG5+4l8v7dpMslhh58TRGuUI1mSC7r8TwPYsUSibxFoppisUMq8tZli52U06kqKaSSMMnm7VSJpMrkM2tkUkXyGQKZNIF0qkC6XSRcjnJ8koPyyvdLK30sLLSTVXWx//3di8wmJ9mKD/N0MAUQ/lpBvtnWD6d4fF/e91GItLC1iEu3rIPmTK4+84fc23XCxz7wjbmjnSTGymy/1cn2foK5wKqjSRys/14vPJGEbmybS9JyFa2bckcFGQdQjeHl9dEqGt7IQk9iHZu2qknzVjLyio89Fe7OPK/RjBSVaolg71vneaVHz1rRugobIlK6Ko24iB1gHIlwYVL2zh9fg+nJ/YwtzAAQHp+iZ6JKXouTJGZWyRRKJHOl3n1l054LlW7Mpnh8T86yHK6lwu3Xkuxt8tRJmGUyWQ2ybdGxGK1QqJSondkhVzfKpVKkocev9u0Z3GF7Y+8RHppFSEliVyFW//6BAvFAWZmh5iZG2JmbpCZuSGKpc3FurpyyyZR56cZzM9skHY6XXSNwJh9ppfn/nYvp4avZ37HKH3M8K5f/AYjw1POY9FIBmomkQfxyO117eWDyCt2O6MQuSEkh3adv3rJXFmmQ+br5T087pDa+aateuXthLsyn2LxQoaerQWy/RWtdP/6tqN56GYf4QndLOusP7eQ53sfv4vF0S2sjAwiE2Zdo1gyCfXWSwwMzNLbO09/3xz9vfNkM2sbBF9eM/jpb99CtWRQNQxWB3oxKhWMUoXB/bPc9tHDJBP60S4T3x3i0ftfwaUD+5AJg9TSKqnVAoW+ro2kM4BMem2dsKcZzk8zOGCSdi7rzOy1Eku1DMW5FKneMomM+cq3c5Pb+e5P38bSSg933vgod936CKlEua4Nt8zLdvLI1e3H45XbbYlLKzfLe5P5VRlnHkfqfpis06ArKYaJOY8LXqsMOu10XynRr7x9Ia6u/hKZvoprXWdavfsKi6r2VWn/gO1YncvnqpYHcFuIS5U9mu+bY3zhOCsvnKOaTLAyMkCxt4tiXxelfBeXZkY5cX5/nS6dTq+RXyf3vt55eLPB2uNJUnNFuqfnTRvSFa59z+lARA7mgloDRyfJTS5w6k23U+rJUerJ1ZUZGbrEttEJ8r1z9PfNke+do6d7yfEEYSeVs98Y5sQXtlItm8lM2+6dZuqmPTx1+HbyfbP8ytu/zPjIBS07dTzyZiMKkdsRZKXIuOPK7Wg7Mtd5N6hWOzbCtxOvqi97er+qjn+/wQjdCjsJOdryIcZodtaTpNdqiQ67fQm3sYSuasP+TtFaGbATvzqMs2a3Wd5sY/9vXOb5vxyHAvRcMKUFI1Nl7wevsOu9s1QqCRaW+phbyDO3mGd+oZ/5xTwXL2/l2KlrzZDCO9f7LZbIFlcYHp/iWCFN/8k5+vvmyffOkckUHLbYkT+4hJGpkl1Y4cDXf8qF269lcfsWAMb6JujKrzK3kOe5IzdTqWxe5gmjTH/vPPm+OfJ9s+T75ujvnSPfN0dP1xKXfpLn2H/bTABa6+/hwbVXUDjcwy0HnuaeOx6omxC2j60VrZZW9NoPyCshQxGDQuWV+6HtyDwsdLJBw5Czw/v28c6Dwkl03oQepC2vxaqU9T089DjJPwzCEDoE89LBm9RH716kUrjAsb8ZpTiXJNldYe+vTbHzPTOmt5uAgf5ZBvpnHW2UKwkWFvuYX8wzu5Bnbj7PwlI/s4tbOPvMXqwvEslmVunvNcm9f92r7u+dZ7BvlkzajBYZvGGJ/HXLzL3UDQXY/thhViYuMHn7AS4vjXHX/od506Hvce7reS4+NUx5JEv3XVDq79q42ZyZ2EWlaiH6RJn04iqJQwXSS6sgYGb/OMlCiV0PP80bP/DDuvmP2liq4CerQHAibTSCyitREPc7baENNHNwmeSMIapFVa6jnYefDPUr769vB9PPzTaiT4qafenp6Cq77ChLYWadpqRy0jPo05JJ9P3rJNvP/EKe+cU8cwv5jezVGrKZ1Q1vur97juqZCqtPGGSLy+x442UGX7vMA4+9kRNn99M9M822h54nuVAEJEZGcs3/cZGdv7SZPbq03MvcYj8LC2Z/R+/fRSHXRak7h0wY9J27zNhTx0jKIm/63DOk6yQ0PW9cVVZn4axme+VBYsod5RuQ7blZdvP7y04zh3h0cwinnV9NCPqGniiIW27RQdwees0ucCflpJCQ9njdnu3C9iP3ZKLCYH6GwfyMY1+5nGB+yST4DflmsZ+Ji9s5snLQLHSN+efF+RX6H5xjoG+ObjnP8uAQJ976asYee4n+M5eoFgTH/2aM8bfMkciaN6J8zwL5ngXYeg6A7D9MMvOTPnMdoFRyIx4+la/ULUegKyGE9chbSeQ6CPLiiSC6ehS0BZlrvSpOp0yTFt5q9ERoUO08TvjJJ0Hlljj0c9j00GsXpY7kAs6JUfDX0a22meXdpacavH4Pr4vXl+iTFYbyMwwpiL5SMZhf9+Tn1j35uYUBzk7uYFmYHn01neLCa25GVJ+h79xlMCQrpzLkDzqTlAAO/MYFHv2TbioFYzOxKVPh4G+eQxj6sgroEXkYjzxuxBm90kq0BZmHRRjvPA7dPAwaGdni5237eedOW9uL0JXHrOgD1LKLo66Llw7hSN2s74yA0UEUIjCSVYYHphkemHbse+zf7uHi0RGKPV2UuzPkpszoGVkWpBUvCK/ZMnDtEq/8iyMc+fw4Cye7yI0UuOb9F9h6hzMByKyjJ6tAPB55zc76MvFNesatk0fJ9jTL6/PbVU3mcSHMSyvifOGzClEjW6JMnLYD/CJcQG/S1Y2kVYTuVd6so0/qZhutG9O9777Mwp9myc4tbWwTCUnv3jW6ttW/bMROMP37V7jzz45tfA/ijbuVV5FimOVs201eaWYEi5+tjQs/iIiEYmbJCGFuQrU+tVa94HXaGbFrjjFfRIao+k8iKS52VT/qyaqqYgykJyG5k1hVaa+zDan8xA1VHyO3LXHgty5iZKokuyoYmSp9+1e57c/OaB1D7fjdJjndZBXVRKfq3NAJQYz7nHXaG6+8EiVtPw687DxzlW6uI8e0YiK03bTzwPJJzHKL2qZwHrpfIlRdfRcvvdY/uEe+1GVNavbndxGrxiTMhb/rXTOMv22WxRNZ0vkK3ePuqfr1fXnIEDF742a5+D1yFaJIJo1O+IkDbUPmqglOHYKNK6olDgSdCI29/5i182ZAJxEqTkL3kl1AHcKoskEFHRlGB3ESRzIrGbpx2b8g8ZE46BOnisj9PHIdRFl7RVU+KOLWynXOiatdPVDC8FrxKEq7tu8JjW6cHoT9JIr2owY/aVovt4SJDlBJLs6xVHuHurKL2bf0lRG8JJia/fZPMxGkb7/j8ZOiHNtcxltHWlG1qTo/m62T22EfV/v4tYLIoYVkbii1bI1IBEUZlS7u344/7Lq5sox9nYvAlrQfGk3oOtAhdGU9BWmobNJp0y+SwI/U69tqDMGHbdf/huRO4rX62jZqSithJg/jSNdvNPk3C20jszQacenmcYQpdqCnn+vIQPY49CB9bvbtLqH4yS+1+uCuq7uh2R67/o0nOIm7kWZYIlffzGNIEow46dnOaHtHMq6oFhXi8s6jot2kFh3E4Z2HuXB0vWEvDz2I7LLRnsYkXRBPvZnQHrOQ0T1xE7m6f0W9GLzyoIg7giXOm0VLyVwltcTWtuImoCPHqG4egft29Outm5t12ovQ7dqkW4iZZx8xELqbdKCjobv1qerX2q6ffqwjQag+zUDQfv2Ox4/Eg+jjuh65TghfGJ283UIRVccVVi+HNvTMlZq4BsGG0c3N/qIjjonQdkAzHvvDeui6GnochF5rW5cIdRE3wUdpT8d2r/aCeONh2t8s40/kYdCOKft+RG53+Ox4WWvmjVqrRUc3b0dt3S9UMQyCxp6r6ujYCvqhlG6hi+BcddFvGQC9kER/Xd3V1iaeJbo3njAkDsFiyHXS9HX7b4a8cjWg7TxzaG5Uiwr2JwGVbh4mTNEPjZBaGhGqGFVuUdbRnPBSPeq6eehBvXQ/6SWIZBHEY28Ugtjjd4xe4+M+P+Ee3um01V8WCXMeNUJeMcvEK7HEcb5EInMhxL8TQjwrhHhaCPE9IcS24AY0d/2KsITfiInQMFJLUEIPg0akHTeS0M1yASQGH88zqvyy0U8LyD1ofzrHE9QbN+sE0Hpj8si1+ooheqUZaftBJRazTDR8Ukp5s5TyVuCbwMcittcSqAahGROh6jqNm+1uJPy8c9B7/NUldGXdgB66H6n79RVUIrGTe1SCj9KeLokH9cbNeuE9crOsznUSbu4lKBqhlceVJGRHJDKXUi5YvnZD45gnbIhi2KiWMGjXidCgUosKoR55Y7oolfU0o1w221TbEsVLr/UXZTJTRci6nzCISuLgN2bRPPK4nADlE10M2norQk91vHKIYQJUCPEJ4IPAPPAGj3IfAj4EsHO8vlsDQTWm+0DYtVoatc55IyZCwyzAFWbdFsC7jksSjhVhJ0RVSUXgXIRKZy2XzTbVa+O4TY5abQH/tdLtF3rUyeU4EIR8/MgtDIm7h3mGI/LQN/8Q8krQUER1neY9afuebUKI7wshnld83gUgpbxPSrkD+ALwe27tSCk/LaW8Q0p5x/BQyAnOkNJHXGu1hEnvD4MwUkscJ00cXofyYtPw6pX2aJZz89CDyC6gJ70E8eaaHWNu71O3X53jiovI3Z+omi/LeSHMOuVhtPK4JBbQ8MyllG/WbOuLwLeAj4e2ps3QqPT+MKspOlcXdF+2tZGILfRQOJfLBXfv2No/6Hno3v27j3lcnnpdHcVZEtVzjxynHsKjdbYRzCNXl9Ujcp0Jz0bJK3EgTASLrsQCEWUWIcQ1UsraK0neCRzWqqepWYd9N6jWOiyKMjrErPMWIqeNGu3ayMW+1nkY+C0vqyJGldzilDGiyy3a9VyIUzcO3WvdFL91XXRJvYYg5G61rVnQftLRIc0YZBWzfDgi1458ClFPxytvRFJRmAgWK6Jq5n8hhDiAyVVngA+HbShO3TxOhHlphf2VcsoyCjIKCj/tXF1HY/EqDUL3tU2lg+vYp+HVe7XnZqsfqXs9GWk/NVgu6KDE3kgE8UTDeuLQPCLXbStMPb2XdzRH9nS06ePJRyJzKeV7o9QPAxW5annwmm8gaueJUB0y1JkMjQONklvc6gV7c1Dwm4/O6ou6pG621zpiDyMjRPHGoblEHlYealT0ShxaeRxoq3T+Rke1xJXer5JaHG8Z0vDOHe1qSC1xaOc6L3+OS25RpfsDoW4E6jcHuWvo4Hzrj99ytXGTes1uN0Qh+qjab1QCh3hI3OwnPJFrecoholeU7cSRAKSMw48msUALyTwhDCoy3MkY5/s6W/l+UD3ZIX7tXLdMGLmlGR466GnoXjbHSeqgT+zOfloRt6wb5RKOyIMibiJv6stQmqSVa70nNbIlDUZca5fHjTDp/VrrpzcgxV+1La7F/0OHlMWol3q1Cd4XnH8Cjd6Y+IU1tho1+3S98Sgeudu5FWUFxCiTt3HJK2GuoWZo5Rv2RO4pAhIivu7jXHgrrvT+MBmhWu2GmICJC7GmX2vaGOw1cI0h9KCk3g7EHtQWXRIPKq2496e+eWvbG0Je0a0Xqq8WaeUbbTes5ZAI+25Q7fYbmN6vvgn4l/FvV8fTDuPR63gW6sQPP4SOSnBJYImL0N21XJ00dxma2BtJ8lH7iYPEvTTyqB65Vjih7lOHwruOI0FIr6/GaOU1tNUEaBCEjWrRRaNiznWgXo+7Mdp5mFBF3bZ148/BOYGpQlAN3a1dr2O2Xshexxzk3aOO/n3OLPsxNuIGoHtD8l/21+uJJ9pkZ9B2dfrxbzvkBGujvP0ga90EtqADT4QZULXn0hztXNceZ1/xyS1KG1wuxLiITedN9loLkAX01nXQSE8+iK3NInLXNiJMeDZSXmlU1EsUr9ys34bQXeM87Ovk4nw/aFwTofGdaMEnYPROzsbKLUEexd0uXrcL2GsM/Eg9yDonVmJvl9cCBrVJ53jDyipBNPJGE3lYeUUFnUnPMDJo0HOo5WSuOwnaiqiWuHpUTYTGpZ2HQVjvPM53NjaC0L3K65C6H4Je7K0i9jD96t6wwnjjQRFpTfuwceia52OYUEQdrVwHfnVaTuZxo5GvkwO96kfedwAABKZJREFUpwGdiVC9vuKRRBoqm0S48JpN6L72aBJ6GA/O7iHHRfBR2w1C4mFllageuatNIZ2LsGhkOG8cjlpbTIDqJhDFOcGptCOm9P7w/ceTRKSTFRrnZGjYZKIgtrnVd0tIcivvN+HqljnqbGd94jWCP9RKKUb/1Xd+8wqNP4Yo8ooKjVp/Rbeew5645swC12gSorwbNOwbiMJC54XPSht02g7pnce1TnIr5BbXNmP00HW1dJ1J0lasWx4GQezU8cS9xi+MR96MCc9GZno2UivXCy64yhHlXZ2tnghVtq31ozVOO2+03BJEP49LcvEjdT8E0UnbidjD3Gj0bmDBSRzCzXPotqFVV5PI43raaJZWvtFf4JavUjTqvZ+BbIhpIlTZdoyPhY2MboHme+hedUCf0ANnOLaA2MP2qXt8YYkuDiJ3tSnkHIluv+2uldcgZAMWkPLtVIgrmOuf2zEMTDXZnHZEZxw6YwCdMYDOGED9GOySUm5RFWoJmbtBCPG4lPKOVtvRanTGoTMG0BkD6IwB6I/Bz43M0kEHHXTwckaHzDvooIMOXgZoNzL/dKsNaBN0xqEzBtAZA+iMAWiOQVtp5h100EEHHYRDu3nmHXTQQQcdhECHzDvooIMOXgZoOzIXQvw7IcSzQoinhRDfE0Jsa7VNzYYQ4pNCiMPr4/A1IUS+1Ta1AkKI9wkhXhBCVIUQPzfhaUKIe4UQR4QQx4UQf9Rqe1oBIcRnhRCXhRDPt9qWVkEIsUMIcb8Q4qX16+BfepVvOzIHPimlvFlKeSvwTeBjrTaoBfgn4EYp5c3AUeCPW2xPq/A88B7gwVYb0iwIIRLAfwLeDlwPvF8IcX1rrWoJ/itwb6uNaDHKwP8lpTwIvBL4iNe50HZkLqVcsHzthiYsy9ZmkFJ+T0pZXv/6MLC9lfa0ClLKl6SUR1ptR5NxJ3BcSnlSSlkEvgS8q8U2NR1SygeBmVbb0UpIKSellE+u/3sReAkYdyvfFkvg2iGE+ATwQWAeeEOLzWk1fhP4cquN6KBpGAfOWb6fB+5qkS0dtAmEELuBQ8AjbmVaQuZCiO8DY4pd90kpvy6lvA+4Twjxx8DvAR9vqoFNgN8YrJe5D/NR6wvNtK2Z0BmHnzOoVoT7uXs67WATQoge4KvAv7IpF3VoCZlLKd+sWfSLwLd4GZK53xgIIX4d+EXgTfJlnAwQ4Fz4ecF5YIfl+3bgQots6aDFEEKkMIn8C1LK/+lVtu00cyHENZav7wQOt8qWVkEIcS/wUeCdUsqVVtvTQVPxGHCNEGKPECIN/Crwv1psUwctgBBCAJ8BXpJS/pVv+XZz+oQQXwUOYL6t7QzwYSnlRGutai6EEMeBDDC9vulhKeWHW2hSSyCEeDfwH4EtwBzwtJTyba21qvEQQvwC8CnMd558Vkr5iRab1HQIIf4OeD3m8q+XgI9LKT/TUqOaDCHEa4EfA8+x+fbKP5FSfltZvt3IvIMOOuigg+BoO5mlgw466KCD4OiQeQcddNDBywAdMu+ggw46eBmgQ+YddNBBBy8DdMi8gw466OBlgA6Zd9BBBx28DNAh8w466KCDlwH+f4AjyO0UuYAgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.optimize as opt\n",
    "import numpy as np\n",
    "\n",
    "points = []\n",
    "\n",
    "def f(p):\n",
    "    x, y = p\n",
    "    z = (1-x)**2 + 100 * (y - x**2)**2\n",
    "    points.append((x, y, z))\n",
    "    return z\n",
    "\n",
    "def fprime(p):\n",
    "    x, y = p\n",
    "    dx = -2 + 2 * x - 400 * x * (y -x ** 2)\n",
    "    dy = 200 * y - 200*x**2\n",
    "    return np.array([dx, dy])\n",
    "\n",
    "init_point = (-2, -2)\n",
    "\n",
    "method = \"fmin\"\n",
    "\n",
    "fmin_func = opt.__dict__[method]\n",
    "if method in [\"fmin\", \"fmin_powell\"]:\n",
    "    result = fmin_func(f, init_point)\n",
    "elif method in [\"fmin_cg\", \"fmin_bfgs\", \"fmin_l_bfgs_b\", \"fmin_tnc\"]:\n",
    "    result = fmin_func(f, init_point, fprime)\n",
    "elif method in [\"fmin_cobyla\"]:\n",
    "    result = fmin_func(f, init_point, [])\n",
    "else:\n",
    "    print(\"fmin function not found\")\n",
    "    sys.exit(0)\n",
    "\n",
    "import pylab as pl\n",
    "p = np.array(points)\n",
    "xmin, xmax = np.min(p[:, 0]) - 1, np.max(p[:, 0]) + 1\n",
    "ymin, ymax = np.min(p[:, 1]) - 1, np.max(p[:, 1]) + 1\n",
    "Y, X = np.ogrid[ymin:ymax:500j, xmin: xmax: 500j]\n",
    "Z = np.log10(f((X, Y)))\n",
    "zmin, zmax = np.min(Z), np.max(Z)\n",
    "pl.imshow(Z, extent=(xmin, xmax, ymin, ymax), origin=\"bottom\", aspect=\"auto\")\n",
    "pl.plot(p[:,0], p[:,1])\n",
    "pl.scatter(p[:, 0], p[:,1], c=range(len(p)))\n",
    "pl.xlim(xmin, xmax)\n",
    "pl.ylim(ymin, ymax)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.70622057 -0.6        -2.5       ]\n",
      "[0.0, -9.126033262418787e-14, 5.329070518200751e-15]\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import fsolve\n",
    "from math import sin\n",
    "\n",
    "\n",
    "def f(x):\n",
    "    x0, x1, x2 = x.tolist()\n",
    "    return [\n",
    "        5*x1 + 3,\n",
    "        4*x0*x0 - 2*sin(x1 * x2),\n",
    "        x1 * x2 - 1.5\n",
    "    ]\n",
    "\n",
    "# f 计算方程组的误差，[1,1,1]是未知数的初始值\n",
    "result = fsolve(f, [1,1,1])\n",
    "print(result)\n",
    "print(f(result))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.70622057 -0.6        -2.5       ]\n"
     ]
    }
   ],
   "source": [
    "from math import cos\n",
    "\n",
    "def j(x):\n",
    "    x0, x1, x2 = x.tolist()\n",
    "    return [\n",
    "        [0, 5, 0],\n",
    "        [8*x0, -2*x2*cos(x1*x2), -2*x1*cos(x1*x2)],\n",
    "        [0, x2, x1]\n",
    "    ]\n",
    "\n",
    "result = fsolve(f, [1,1,1], fprime=j)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "import pylab as pl\n",
    "\n",
    "\n",
    "x = np.linspace(0, 10, 11)\n",
    "y = np.sin(x)\n",
    "\n",
    "xnew = np.linspace(0, 10, 101)\n",
    "pl.plot(x,y, 'ro')\n",
    "for kind in ['nearest', 'zero', 'slinear', 'quadratic']:\n",
    "    f = interpolate.interp1d(x, y, kind=kind)\n",
    "    ynew = f(xnew)\n",
    "    pl.plot(xnew, ynew, label=str(kind))\n",
    "\n",
    "pl.legend(loc='lower right')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = np.linspace(0, 10, 20)\n",
    "y1 = np.sin(x1)\n",
    "sx1 = np.linspace(0, 12, 100)\n",
    "sy1 = interpolate.UnivariateSpline(x1, y1, s=0)(sx1)\n",
    "\n",
    "import pylab as pl\n",
    "pl.plot(x1,y1, 'ro', label=\"Data Points\")\n",
    "pl.plot(xnew, ynew, label=\"spline Linear\")\n",
    "pl.legend(loc=\"lower right\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x2 = np.linspace(0, 20, 200)\n",
    "y2 = np.sin(x2) + np.random.standard_normal(len(x2))*0.2\n",
    "sx2 = np.linspace(0, 20, 2000)\n",
    "sy2 = interpolate.UnivariateSpline(x2, y2, s=8)(sx2)\n",
    "\n",
    "import pylab as pl\n",
    "pl.plot(x2,y2, 'ro', label=\"Data Points\")\n",
    "pl.plot(xnew, ynew, label=\"spline Linear\")\n",
    "pl.plot(sx2, sy2, label=\"Univariate Linear\")\n",
    "pl.legend(loc=\"lower right\")\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "import pylab as pl\n",
    "\n",
    "def func(x, y):\n",
    "    return (x+y)*np.exp(-5.0*(x**2 + y**2))\n",
    "\n",
    "# X-Y轴分为15*15的网格\n",
    "y, x = np.mgrid[-1:1:15j, -1:1:15j]\n",
    "fvals = func(x, y)\n",
    "\n",
    "pl.imshow(fvals, extent=(-1,1,-1,1), origin=\"bottom\", aspect=\"auto\")\n",
    "pl.xlim(-1,1)\n",
    "pl.ylim(-1,1)\n",
    "pl.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 二维插值\n",
    "newfunc = interpolate.interp2d(x, y, fvals, kind='cubic')\n",
    "\n",
    "# 计算100*100的网格上的插值\n",
    "xnew = np.linspace(-1,1,100)\n",
    "ynew = np.linspace(-1,1,100)\n",
    "fnew = newfunc(xnew, ynew)\n",
    "\n",
    "pl.imshow(fnew, extent=(-1,1,-1,1), origin=\"bottom\", aspect=\"auto\")\n",
    "pl.xlim(-1,1)\n",
    "pl.ylim(-1,1)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "\n",
    "def func(x, y):\n",
    "    return (x+y)*np.exp(-5.0*(x**2 + y**2))\n",
    "\n",
    "\n",
    "# 计算曲面上的100个随机分布的点\n",
    "x = np.random.uniform(-1.0, 1.0, size=100)\n",
    "y = np.random.uniform(-1.0, 1.0, size=100)\n",
    "xmin, xmax = np.min(x), np.max(x)\n",
    "ymin, ymax = np.min(y), np.max(y)\n",
    "\n",
    "fvals = func(x, y)\n",
    "# 使用RBF进行插值运算\n",
    "newfunc = interpolate.Rbf(x, y, fvals, function='multiquadric')\n",
    "ynew, xnew = np.mgrid[-1:1:100j, -1:1:100j] # 插值结果的网格\n",
    "fnew = newfunc(xnew, ynew)\n",
    "\n",
    "pl.imshow(fnew, extent=(-1,1,-1,1), origin=\"bottom\", aspect=\"auto\")\n",
    "pl.xlim(-1,1)\n",
    "pl.ylim(-1,1)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用RBF进行插值运算\n",
    "newfunc = interpolate.Rbf(x, y, fvals, function='multiquadric')\n",
    "ynew, xnew = np.mgrid[-1:1:100j, -1:1:100j] # 插值结果的网格\n",
    "fnew = newfunc(xnew, ynew)\n",
    "truevals = func(xnew, ynew)\n",
    "\n",
    "pl.imshow(truevals, extent=(-1,1,-1,1), origin=\"bottom\", aspect=\"auto\")\n",
    "pl.xlim(-1,1)\n",
    "pl.ylim(-1,1)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
